InvestorQ : What happens to the value of a put option when the interest rates go up to a higher level?
Katherine Gonsalves made post

What happens to the value of a put option when the interest rates go up to a higher level?

Answer
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Tisha Malhotra answered.
1 year ago


Let us look at a live example to understand the impact of an increase in interest rates on the value of the put option. Let us take the case when the interest rate goes up by 100 basis points from 5% to 6%.

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

120

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.08333

Number of periods to Exercise in years (t)

0.08333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

6.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

30.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.3766

s*t^0.5

0.0866

s*t^0.5

0.0866

d1

-0.3800

d1

-0.3703

d2

-0.4666

d2

-0.4569

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.3556

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

40.2803

Value of Put

6.8345

Value of Put

6.7642

The strike price pertains to the expiry date. For example, when you buy a 125 strike put option when the market price is Rs.120 then it is the right to sell the stock at Rs.125 on the last Thursday of the month, which is the F&O expiry. But the market price pertains to the current date. Hence to make them comparable, you need to calculate the present value of the excise price or the strike price. This present value discounting is done based on the interest rates and that is why interest rates are relevant to the calculation of the put option value. In the above instance you can see that the interest rates have moved up by 100 basis points and as a result the present value of the excise price as shown in the above table has come down. Being a put option, this narrows the positive gap between the stock price and the market price or it widens the negative gap between the stock price and the market price and therefore ends up making the put option less valuable. It can be seen that the impact of the 100 bps change in the interest rates on the value of the call option is not very significant and that is more because it is a second level impact.