What happens to the value of the call and put options under Black & Scholes when the interest rates in the economy move up?
Answer
Answer
You may wonder how do interest rates in the economy impact the value of the call and put options. The Black and Scholes captures the risk free rate on bank deposits as the base rate for calculating the present value. Since the strike price pertains to a future date (which is the last Thursday of either the current month or the next month), a rise in interest rates reduces the present value of the strike price of the option. Check out the table below:
Inputs
Inputs
Stock Price Now (Ps)
? 1,110
Stock Price Now (Ps)
? 1,110
Standard Dev - Annual (s)
30.00%
Standard Dev - Annual (s)
30.00%
Risk free Rate - Annual (R)
6.00%
Risk free Rate - Annual (R)
7.00%
Exercise Price (E)
? 1,100
Exercise Price (E)
? 1,100
Time To Maturity - Years (T)
0.0833
Time To Maturity - Years (T)
0.0833
Dividend yield (d)
1.00%
Dividend yield (d)
1.00%
Outputs
Outputs
d1
0.196
d1
0.206
d2
0.109
d2
0.119
N(d1)
0.578
N(d1)
0.581
N(d2)
0.544
N(d2)
0.547
Call Price (Vc)
? 45.77
Call Price (Vc)
? 46.27
-d1
-0.196
-d1
-0.206
-d2
-0.109
-d2
-0.119
N(-d1)
0.422
N(-d1)
0.419
N(-d2)
0.456
N(-d2)
0.453
Put Price (Pp)
? 31.21
Put Price (Pp)
? 30.79
In the above illustration we have increased the risk free rate of return from 6% to 7%. Why does the value of the call increase in this case? Say the strike price of the option is Rs.100 and the market price of the stock is Rs.105. In this case the intrinsic value of the call option is Rs.5. If the interest rates go up then the present value of the strike price will come down below Rs.100. That will increase the intrinsic value off the option and thus enhance the value of the call option. In case of put option, the reverse operates and that is why the option value falls when the risk free rate goes up. You will notice that despite the rate of interest going up by 1%, the value of the call option and put option has been impacted only marginally. That is because; we are talking of a 1% change in a 1 month option where the overall impact is quite small.