Real options

We have been almost entirely concerned with the valuation of derivative dependent on financial assets. Real assets include land, building, plant, and so on.Often there are embedded options.Valuation is difficult because market prices are not readily available.

We start by explaining the traditional approach to evaluating investments in real assets and their shortcomings.


The traditional approach to valuing a potential  capital investment project is known as the “net” present value” or NPV  approach. The NPV of a project is the present value of its expected future incremental cash inflows and outflows. The discount rate used to calculate the present value is a “risk-asjusted” discount rate, chosen to reflect the risk of the project. As the riskness of the project increases, the discount rate also increases.

As an example consider an investment that costs $100 million. If the risk-adjusted discount rate is 12%,the net present value of the investment is(in million of dollars)

-100+\frac{25}{1.12}+\frac{25}{1.12^{2}}+\frac{25}{1.12^{3}}+\frac{25}{1.12^{4}}+\frac{25}{1.12^{5}}= -9.88

A negative NPV, such as the one we have just calculated,indicates that the project will reduce the value of the company to its shareholder and should not be undertake. A positive NPV indicates that the project should be the undertaken because it will increase shareholder wealth.

The risk adjusted discount rate should be the return required by the company, or the company’s shareholder, on the investment. This can be calculated in a number of ways. One approach often recommended involves the capital asset pricing model. The steps are as follows.

1) Take a sample of companies whose main lines of business is the same as that of the project being contemplated.

2) Calculate the betas of the companies and average them to obtain a proxy beta for the project.

3) Set the requested rate of return equal to the risk-free rate plus the proxy beta times the excess return of the market portfolio over the risk-free rate.

One problem with the traditional NPV approach is that many projects contain embedded options. Consider, for example, a company that is considering building a plant to manufacture a new product.

Often the company has the option to abandon the project if things do not work out well. It may also have the option to expand the plant if demand for the output exceeds expectations. These options usually have quite different risk characteristics from the base project and require different discount rate.

This involved a stock whose current is $20. In three months ‘ time the price will be either $22 or $18. Risk neutral valuation shows that the value of a three-month call option on the stock with a strike price of 21 is 0.633.

The expected return required on the call option is 42.6%.In practice it would be very difficult to estimate these expected returns directly in order to value the option on real assets.

There is no easy way of estimating the risk-adjusted discount rates appropriate for cash flows when they arise from abandonment, expansion , and other options. This is the motivation for exploring whether the risk-neutral valuation principal can be applied to options on real assets as well as options on financial assets.

Another problem with the traditional NPV approach lies in the estimation of the appropriate risk-adjusted discount rate for the base project. The companies that are used to estimate a proxy beta for the project in the three-step procedure above have expansion options and abandonment options of their own. Their betas reflect these options and may not therefore be appropriate for estimating a beta for the base project.


Consider an asset whose price, f , depends on variable 0 and time t. Assume that the process followed by 0 is.

\frac{d\theta }{\theta }=m dt+s dz


Where dz is a Wiener process. The parameters m and s are the expected growth rate in \Theta and t. The variable \Theta need not be a financial variable. It could be something as far removed from financial markets as the temperature in the Centre of New Orleans.

The asset price f follows a process of the form

df= \mu f dt+\sigma fdz

Extension of Traditional Risk-Neutral valuation

Any solution to equation for s is a solution to equation for \theta, and vice versa , when the substitution

q= r-m+ \lambda s

Using risk- neutral valuation. This involves setting the expected growth rate of a equal to r-q and discounting expected payoffs at the risk-free interest rate. It follows that we can solve by setting the expected growth of \theta equal to

r= (r-m+ \lambda s)= m-\lambda s

and discounting expected payoffs at the risk-free interest rate.


Traditional methods of business valuation, such as applying a price earnings multiplier to current earnings, do not work well for new business. Typically a company ‘s earnings are negative during  it’s really years as it attempt to gain market share and establish relationship with customers. The company must be valued by estimating future earnings and cash flows under different scenarios.

The company ‘ future cash flows typically depend on a number of variables such as sales, variable costs as a percent of sales, fixed costs, and so on. Single estimates should be sufficient for outlined in the previous two sections. A Monte Carlo simulation can then be carried out to generate alternative scenario for the net cash flows per year in a risk-neutral world.  It is likely that under some of these scenarios the company does very well and under others it becomes bankrupt and ceases operations.

The simulation must have a built-in  rule for determining when bankruptcy happens. The value of the company is the present value of the expected cash flow in each year using the risk -free rate for discounting.











Mechanics of option market

          Fundamental and types of option

The option is fundamentally different from the forward, future, and swap contracts. An option gives the holder of the option the right to do something. The holder of the option does not have to exercise this right. By contrast in a forward contract, future, or swap contract.

In mechanics of option explained. The two parties have committed themselves to some action underlying assets. These assets included stock, stock indices, foreign currencies, and futures contracts.

i)Stock option:-Option trade on more different stocks worldwide stock exchange one contract gives the holder the right to buy or sell a share at a specified price.

ii)Foreign currency option:-The major exchange trading foreign currency option is the Philadelphia stock exchange. The size of one contract depends on the currency.

iii)Index option:-Many different index options currently trade throughout the world. The most popular exchange is the S&P500 Index, Chicago board(CBOE) option exchange, Boston options exchange, Eurex exchange, NYSE Arca, Index national securities exchange(ISE).

iv)Future option:-In future option, The underlying asset is the futures contract. The future contract normally matures shortly after the expiration of the option. Future options are now available for most of the assets in which future contracts traded and normally traded on the same exchange as the future contract.                                  

                     Specification of stock option

Stock option specification explained the expiration date the strike price, terminology fix option, dividends stock splits.

i)Expiration dates:-One of the item used to describe a stock option in the month in which the expiration date occurs.

ii)Strike price-Strike price is that price where stock option exercised on the maturity date, usually maturity date last Thursday of the month in European option.

iii)Terminology:-For any given time, Many different options contracts may be a trading option referred to as in the money at the money or out the money. An in-the-money option would. Give the holder a positive cash flow if it exercised immediately.

Similarly, an at the money option would lead to a zero cash flow, if it were exercised immediately, and the out-of-the-money option would lead to negative cash flow if it were exercised immediately.

iv)Fiex option:-Fiex option on equities and equity indices. These are an option where the traders on the floor of the exchange agree to nonstandard terms. These nonstandard terms can involve a strike price or an expiration date that is different from what is usually offered by the exchange.

It can also involve the option of being European rather than American.Flex options are an attempt by options exchange to regain business from the over-the-counter market. The exchange specifies a minimum size for flex option trades.

v)Dividend:-The early over-the-counter option dividend protected. If a company declared a cash dividend the strike price for options on the company’s stock was reduced on the ex-dividend day by the amount of the dividend.

Exchange-traded options are not generally adjusted for cash dividend occurs, there is no adjustment to the term of the option contract.

vi) Stock split:-Exchange-traded options adjusted for stock splits. A stock split occurs when the existing share is “split” into more shares. For example, in a 3-for-1 stock split, three new shares issued to replace each existing share.

Because a stock split does not change the assets or the earning ability of a company, we should not expect it to have any effect on the wealth of the company’s shareholders.

vii)Position limits and exercise limits: -A position limit for option contracts. This defines the maximum number of option contracts that an investor can hold on one side of the market.

For this purpose, long calls and short puts considered to be on the same side of the market. Also, short calls and long puts considered to be on the same side of the market. The exercise limit equals the position limit.

Future contract

A futures contract is an agreement between two parties to buy or sell an asset. This contract executes at a certain time in the future for a certain price. Unlike forward contracts, futures contracts normally traded on an exchange. To make trading possible, the exchange specifies certain standardized features of the contract.

As two parties to the contract do not necessarily know each other. The exchange also provides a mechanism that gives the two parties a guarantee that the contract will be honored. The largest exchange on which futures contracts are traded in the Chicago Board of trade(CBOI) and Chicago Mercantile Exchange(CME).On these and other exchanges throughout the world, a very wide range of commodities and financial assets form the underlying assets in the various contracts.

One way in which a futures contract is different from a forward contract is that an exact delivery date is usually not specified. The contract referred to by its delivery months, and the exchange specifies the period during the month when delivery made. For commodities, the delivery period is often the entire month. The holder of the short position has the right to choose the time during the delivery period when it will make delivery.

How future contract works

The futures contract is an agreement to buy sell an asset at a certain time in the future for a certain price.
Future trading is to enter into contracts to buy or sell financial instruments dealing in commodities or other financial instruments.
Financial futures contracts exist to provide risk management to partial risk and uncertainty in the form of price volatility and opportunism are major factors giving rise to future trading. Future trading evolved out of autonomous forward contracting by merchants dealers and process.

Future v/s forward contract
1)Future contract in a competitive arena by “open outcry” of bids, offers, and amounts.
A forward contract done by telephone with participants generally dealing directly with broker-dealers.

2)Contract terms standardized with all buyers and sellers negotiating only with respect to price.
All contract terms are negotiated privately by the parties.

3)Participants include banks, corporations financial institutions,individual investors, and speculators.
participants are primarily institutions dealing with one other and other interested parties dealing through one or more dealers.

4)Long and short positions usually liquidated easily.
Forward positions not as easily offset or transferred to other participants.

5)Settlements normally made in cash, with only a small percentage of all contracts resulting in actual delivery.
The most transactions result in delivery.


Forward contract

A forward contract is a particular simple derivative. It is an agreement to buy or sell assets at a certain future time for a certain price. A forward contract can be contrasted with a spot contract, which is an agreement to buy or sell an asset today. It is traded in the over-the-counter market. Usually between two financial institutions or between a financial institution and one of its clients.
One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. The other party assumes a short position and agrees to sell the asset on the same date for the same price.


Payoff from long position

short position payoff

How forward contracts works

A forward contract specify the delivery of security at some future date.A forward price determined at the time the contract entered into and it is a set at a level so that the contract has no initial monetary value .

The parties to this, the buyer and the seller retain the flexibility to designate the grade and the quantity of the goods to be delivered as well as the time and place of delivery.

Forward vs Future contract

A futures contract has essentially the same characteristics as a forward cbut differs in four aspects that affect the ease with which traded relative to this.

Both contracts are agreements to buy or sell an asset for a certain price at a certain future time. A forward contract standardized contract traded on an exchange.

Forward v/s future contract

1)Forward contracts traded on over the counter market.
Future contract traded on an exchange.

2)Forward contract, not a standardized contract.
Future contract standardized contract.

3)Forward contract has unspecified delivery date.
Future contract has range of delivery date.

4)Forward contract settled at end of contract
Future contract settled daily.

5)Final cash settlement usually takes place.
Contract usually closed out prior to maturity.









Stock option

Options traded both on the exchange and in the over-the-counter market. Call option and put option. Now we will discuss the call option.

                             Call option

Call option gives holder to right buy the underlying the price of an option to purchase one share is $5.The initial investment is $500.The option is European.

The investor can exercise only on the expiration date. If the stock price on this date is less than $60. The investor will clearly choose not to exercise. In these circumstances. The investor loses the whole of the initial investment of $500.If the stock price is above $60 on the expiration date the option exercised.

Suppose that the stock price is $75.By exercising the option, the investor is able to buy 100 shares for 60 per share. If the share sold immediately investor gain of $15 per share or $1500 ignoring transaction costs. When the initial cost of the option taken into account, the net profit to the investor is $1000.

Profit from buying a call option

                                          Put option

A put option gives the holder the right to sell the underlying asset by a certain date for certain price. The purchase of a put option is hoping that stock price will decrease.

An investor who buys a European put option to sell 100 shares with strike price of $90.Suppose that the current stock price is $85.Expiration date of the option is in three months and the price of option to sell one share is $7.

The initial investment is $700 Because the option is will be exercised only if the stock price is below$90 at the expiration date. Suppose that the stock price is $75 on this date.

The investor can buy 100 share for $75 per share and under the term of the put option sell the same share for $90 to realize a gain of $15 per share or $1500.

When the $700 initial cost of the option is taken into account. The investor’s net profit is $800.There is no guarantee that the investor will make a gain. If the final stock price is above $90, the put option expires worthless, and the investor loses $700.

Profit from buying a put option




Put-call parity

  To understand put-call parity. We assume. We have two  portfolios. Portfolio A and Portfolio B

One European call option plus an amount of cash equal to  ke^{-rt}   portfolioB: One European put option plus one share.Both are worth.max  (S_{r},k)

At  expiration of the options. Because the option is European, they can not be exercised prior to the expiration date. The portfolio must, therefore, have identical values.
c+ ke^{-rt}=p+S_{o}

This relationship is known as put-call parity. It shows that the value of European call with a certain exercise price and exercise date can be deduced from the value of a European put with the same exercise date and vice-versa. If equation 2nd does not hold.

There is arbitrage opportunity. For example, the stock price is $31, the exercise price is $30, the risk-free interest rate 10% per annum, the price of three-month European call option is $3,and the price of a three-month European put option is 2.25.

 c+Ke^{-rt}=3+30e^{-0.1\times3/12 }=$32.26

Portfolio B is overpriced relative to portfolio A.The correct arbitrage strategy  to buy the securities in portfolio B.The strategy involves buying the call and shorting both the put and the stock, generating a positive cash flow of

upfront,when invested at the risk-free interest rate;this amount grows to 30.25e^{0.1\times 0.25}=$31.02 in three months.

If the stock price at expiration of the option is greater than $30, the call will be exercised.If it is less than $30, the put will be exercised.In either case, the investor ends up buying one share for $30.This can be used to close out the short position. The net profit is therefore
For an alternative situation, suppose that the call price is $3 and the put price is $1.In this case.
c+Ke^{-rT}=3+30e^{-0.1\times 3/12}=$32.26

Portfolio A is overpriced relative to portfolio B.An arbitrageur can short the securities in portfolio A and buy the securities in portfolio B to lock in a profit.The strategy involves shorting the call and buying both the put and the stock with an initial investment of

when the investment is financed at the risk-free interest rate, repayment of 29_{e}^{0.1\times 0.25}  = $29.73 is required at the end of the three months. As in the previous case, either the call or the put will be exercised. The short call and long put option position, therefore, leads to the stock sold for $30.00.The net profit is therefore


Now Put-call parity for European future option on the assumption that there is no difference between the payoffs from future and forward contracts.

Consider European call and put future options both with strike price k and time to expiration T. We can form two portfolio
Portfolio C: European call future option plus an amount of cash equal to Ke^{-rt}
Portfolio D: European put future options plus a long future contract plus an amount of cash equal to F_{o}e^{-rt}.
In portfolio A the cash be invested at the risk-free rate,r, and will grow to K at time T.Let F_{T} be the futures price at maturity of the option in portfolio C is exercised and portfolio C is worth F_{T}. If  F_{T}>K, the call option in portfolio C is exercised and portfolio C is worth F_{T}. If F_{T}\leq K, the call is not exercised and portfolio C is worth k.The value of portfolio C at a time is therefore
In portfolio D the cash can be invested at the risk-free rate to grow to F_{0} at time T. The put option provides a payoff of max(K-F_{T},0).The future contract provides a payoff of F_{T}-F_{0}.The value of portfolio D at time T is therefore
Because the two portfolio have the same value at time T and there are no early exercise opportunities,it .follows that they are worth the same today.The value of portfolio C today is
where c is the price of the call future option.The marking-to-market process ensures that the future contract in portfolio D is worth zero today.Therefore D is worth
where p is the price of the put future option.Hence

Interest rate market

For any given currency many different rates are regularly quoted.These include mortgage rates prime borrowing rates, deposit rates.Interest rate applicable on the credit risk situation.Higher the credit risk higher Interest rate .In this post we discuss about three rate which is important for option and future market .

Treasury rate-: Treasury rate applicable to borrowing by a government in its own currency  U.S.treasury  rates are the rates at which the U.S. government can borrow in U.S.dollar. Indian treasury rates are the rate at which  Indian government can borrow in Indian Rupee thats why their is no chance that government will default on an obligation denominated in its own currency.

LIBOR rate– Large international bank actively trade with each other.1 month 3 month,6 month and 12 month deposits denominated in all the world’s major currencies.If at particular time .Citi bank bid rate and offer rate to other banks for six month deposit  in australian dollar .The bid rate is known as the London Interbank Bid Rate(LIBID).The offer rate is known as the London Interbank offer rate or LIBOR.The rates are determined in trading between bank and change as economic condition change .If more bank borrow funds than lend funds.LIBID and LIBOR increases, If the reverse is true they decrease .LIBOR rates are generally higher than the corresponding treasury rates because they are not risk free rates.There is always a chance bank borrowing money will default large financial institution and banks tend to use the LIBOR rates rather than the treasury rate.The reason is that financial institution invest surplus fund in the LIBOR market and borrow to meet their short term funding requirement in the market.

Repo rate -Repurchase agreement(repo). This is a contract  where an investment dealer who owns securities are to sell them to another.Company now and buy them back later at slightly higher price.Difference between the price at which the securities are sold and the price at which they are repurchase is the interest earns. the loan involve very little credit risk.If the original owner of  the securities does not honor the agreement the lending company simply keeps the securities.If landing company does not keep to its side of agreement.The original owner of the securities keep the cash .Most common type repo is an overnight repo,longer term Repo called term repo.

Zero rates– Zero coupon rate of interest earned an investment that started today and lasts for n years all the investment and principal is realized at the end of n years.There are no intermediate  payments.The n year zero rates is sometimes also referred to as the n-year spot rates

Forward Market

Forward market is an over the counter market.lets understand what is OTC market?Over the counter market Over the counter market is an important alternative to exchange and measured in term of total volume and trading.It is a telephone and computer linked network of dealers who do not physically meet.Trades are done between a financial institution and one of its corporate clients.Trades in the over-the-counter market are typically much larger than trade in the exchange traded market .

Now understand what is forward contracts?
A forward contract is particularly simple derivative.It is an agreement to buy or sell an asset at a certain future time for certain price.

“Forward contract is traded in the over-the-counter market.Usually between two financial institution and one of its clients.” forward contract on foreign exchange are very popular most large bank have “forward desk” within their foreign exchange trading room.

Forward in the debt market.
The forward contracts that are found in the debt market are.
1) Forward Interest rate contracts:-Forward interest rate for a future period of time implied by the rates prevailing in the market.Forward interest rates are the rats of interest implied by current zero rates for periods of time in the future.

2)Repurchase agreements(Repo rate):-Repurchase agreement a contract where an investment dealer who owns securities agrees to sell them to another company now and buy them back letter at slightly higher price.
The difference between the price at which the securities are sold and the price at which they are repurchase is the interest it earns.The interest rate is referred to as the repo rate.

Type of repurchase agreement .
1) Open repurchase agreement :-Open repurchase agreement is where there no agreed termination date.Both parties have the option to terminate the agreement without notice .Rate of these agreement is usually a floating rate.
2)Fixed term repurchase agreement-Where the rate and the term are agreed at the outset of the agreement.The term of repos usually ranging from a day to a few months.

3)Forward rate agreement:-A forward rate agreement is an over-the-counter agreement that a certain interest rate will apply to a certain principal during a specified future period of time. FRA is agreement between two parties based on a notional amount for an contract period.This is a contract where interest rate is fixed for future.FRA hedge the interest rate risk.its consist of one to six month.







Credit derivatives

Credit derivative are contracts where the payoff depends on the creditworthiness of one or more commercial or sovereign entities , credit derivative allow companies to manage their credit risk actively.

According to the definition, the use of the derivative security determines whether the derivative is a credit derivative or not. A simple derivative contract like a forward contract on a defaultable bond may be credit derivative to one counter party risk.(because he intends to use it to manage credit risk) and not a credit derivative to another.

Credit derivative bilateral contract between debtor and creditor.It allows the creditor to transfer the risk of the debtor default to a third party.

What are derivatives?
As the name suggests derivatives are based on or derived from an underlying  asset and the way to evaluate derivatives is to value an equivalent structure of assets (or liabilities)
All derivatives are redundant because they can be replicated with a bundle of straight forward basic operations.Derivative have one decisive advantage over the underlyining bundle of assets and that is transaction costs.
It is not an uninteresting perspective to look at stocks and bonds as primitive options.

How credit derivative works
A credit derivative can remove the risk of default. Lender and borrower both can use it. By use of credit derivative banks has the right to transfer the risk of default to the third party.

Type of credit derivative
Credit default swap(CDS)
Total return swap
Credit spread option

Credit default swap->A credit default swap (CDS) is a contract that provides insurance against the risk of default by a particular company.The company is known as the reference entity and default by the company is known as the reference entity and default by the company is known as a credit event.The buyer of the insurance obtains the right to sell a particular bond issued by the company for its par value when a credit event occurs. The bond is known as the reference obligation and the total par value of the bond that can be sold is known as the swap’s notional principal.
The buyer of CDS makes periodic payments to the seller until the end of the life.If the CDS or until a credit event occurs.

Credit derivative allow companies to manage their credit risk actively.

a)Binary credit default swaps-> Binary credit default swap can be quite sensitive to the expected recovery rate estimate. This is structured similarly to a regular credit default swap. Except that the pay of is a fixed dollar amount. In this case, the expected recovery rate affects the probability of default but not the payoff. As a result, the credit defaults spread is quite sensitive to the recovery rate.

b)Basket credit default swaps-> In a basket credit default swap there are a number of reference entities.An add-up basket credit default swaps.One an each reference entity.A first to default swap provides a payoff only when the first reference entity defaults.

2)Total return swaps->A total return swap is an agreement to exchange the total return a bond or other reference assets for LIBOR plus a spread. The total return includes coupons interest and the gain or loss on the assets over the life of the swap.A total return swap always used as a financing tool.

The payer retains ownership of the bond swap and has much less exposure to the risk of the receiver defaulting than it would have if it had lent money to the receiver to finance the purchase of the bond. The total return swap is similar to repos. They are structured to minimize credit risk when money is borrowed.
There are number of variation on the change  in value of the bond.there physical settlement where the payer exchange the underlying asset  for the notional principal at the end of the life of the swap.Sometimes the change in value payments are made periodically rather than all at the end.

3)Credit spread options->Credit spread option are options where the pay off depends on either  a practical credit spread or the price of a credit-sensitive asset. Typically the options are structured so that they ease to exist if the underlying assets default. If a trader wants protection against both an increase in a spread and a underuritylying asset defaults then both credit spread option and another instrument such as credit default swap are required one type of credit spread option is defined so that it has a payoff of.
where S_{T} is a particular credit spread at option maturity
K=Stike spread

Another type of credit spread option is a European call or put option on a credit sensitive asset such as a floating rate note.










Derivative and risk management

A company faces several kind of risk.Unanticipated change in selling price,cost taxes,demand,interest rate technology fluctuated profitability of a firm.Sometime managers are not able to reduce risk.They try many strategies.All financial difficulties and risk can reduce their risk entering into financial contracts.

Risk hedging by derivatives 

The topic will explain what is derivatives and how to hedge risk by it.Derivatives mans those items that do not have their own independent value it is a financial instrument derived from some other asset which is called underlying asset. In the firm risk always remain firm can avoid cash flow fluctuation by reducing the risk.Itwill increase value of their asset or investment.Firm always seeking the way to reduce risk derivative are tools to reduce a firm’s risk exposure.

Firm risk can hedge by four derivatives these are future,forward,option and swap.

Hedging by option

Option is one of  the most complex financial instrument.Firm can use option to minimize risk.Option has two type call option and put option.If a firm purchase new product in large quantity most of firm’s capital invested.In this type of deal always risk remain,to reduce risk firm can buy option in stock market only premium have to pay if strike price more than spot price firm will make profit but unfortunately if price opposite each other firm will loose option premium amount.

Hedging by forward

Forward contract is non-standardized contract between two parties.In this contract assets buy or sell in future at predetermined price.Forward contracts are similar to option in hedging but there is a difference both buyer and seller are bounded by the contract both must have exercise the contract at the agreed price on the specified due date forward contracts are flexible suits the need of buyer and seller.We can enter into a forward contract for any good commodities and asset.We can choose any delivery date and quantity of goods. 

Hedging by future 

Future contract are same as a forward contract.Future contracts are not different from forward contracts.The difference is in terms of standardisation and method of operation.Future contracts have standardised contract size and they trade only the organised exchanges.In future contract both parties should agreed as same price,duedate and time.In future contracts like in the forward contracts one party will loose and other will gain.

Hedging by swap

Swap are same as future and forward contracts.It is also providing hedge against risk.Swap also a agreement between two parties called counter parties most popular swap are currency swap and interest rate swap.This two swap can be combined when interest on loan can be swapped between two currency.

1)Currency swap :- In currency swap exchange of cash payment done between two currency most of companies want overseas investment but they find difficulties entering in new market currency swap is an alternative to overcome this problem.

2)Interest rate swap:-The interest rate swap allows a company to borrow capital at fixed and exchange its interest payment at floating rate or fixed rate LIBOR is the market determined interest rate for banks to borrow from each other in the euro dollar market.