Risk -free interest rate is a rate obtainable from a default-risk from government securities. An investor assuming risk from her investment requires a risk premium above the risk -free interest rate.
Risk-free rate is compensation for time and risk premium for risk. Higher the risk of action, the higher will be the risk premium leading to higher required return on that action. A proper balance between return and risk should be maintained to maximize the market value of a firm’s share.
The risk-free interest rate affects the price of an option in a less clear-cut way. As the interest rate in the economy increase, the expected return required by an investor from the stock tends to increase also, the present value of any future cash flow received by the holder of the options decrease. The combined impact of these two effects is to decrease the value of the put option and increase the value of call options.
We are assuming that interest rates change while all other variables stay the same. In particular, we are assuming that interest rates change while all other variables stay the same. In practice, when interest rates (fall), stock prices tend to fall(rise).
The net effect of an interest rate increase and the accompanying stock price decrease can be to decrease the value of call option and increase the value of a put option, Similarly, the net effect of an interest rate decrease and the accompanying stock price increase can be to increase the value of a call option and decrease the value of a put option.