InvestorQ : What happens to the value of the call and put options under Black & Scholes when the interest rates in the economy move down due to RBI repo rate cut?

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 fall in interest rates increases the present value of the strike price of the option. Check out the table below:

Inputs

Inputs

Stock Price Now (P_{s})

? 1,110

Stock Price Now (P_{s})

? 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)

4.00%

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

0.177

d2

0.109

d2

0.090

N(d1)

0.578

N(d1)

0.570

N(d2)

0.544

N(d2)

0.536

Call Price (V_{c})

? 45.77

Call Price (V_{c})

? 44.78

-d1

-0.196

-d1

-0.177

-d2

-0.109

-d2

-0.090

N(-d1)

0.422

N(-d1)

0.430

N(-d2)

0.456

N(-d2)

0.464

Put Price (P_{p})

? 31.21

Put Price (P_{p})

? 32.05

In the above illustration we have reduced the risk free rate of return from 6% to 4% in tune with the cut in the reference repo rate by the RBI in its latest credit policy. Why does the value of the call fall 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 down then the present value of the strike price will go up to a level above Rs.100. That will reduce the intrinsic value off the option and thus also reduce the value of the call option. In case of put option, the reverse operates and that is why the option value rises when the risk free rate goes down. You will, however, notice that despite the rate of interest going down by 2%, the value of the call option and put option has been impacted only marginally. That is because; we are talking of a 2% change in a 1 month option where the overall impact is quite small. That is the reason; the rate changes do not have a major impact on the value of the call and the put option.

Lavanya Subramaniananswered.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 fall in interest rates increases the present value of the strike price of the option. Check out the table below:

InputsInputsStock Price Now (P

_{s})? 1,110

Stock Price Now (P

_{s})? 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)

4.00%

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%

OutputsOutputsd1

0.196

d1

0.177

d2

0.109

d2

0.090

N(d1)

0.578

N(d1)

0.570

N(d2)

0.544

N(d2)

0.536

Call Price (V_{c})? 45.77

Call Price (V_{c})? 44.78

-d1

-0.196

-d1

-0.177

-d2

-0.109

-d2

-0.090

N(-d1)

0.422

N(-d1)

0.430

N(-d2)

0.456

N(-d2)

0.464

Put Price (P_{p})? 31.21

Put Price (P_{p})? 32.05