Option Greeks: Rho
Suppose you entered into an option contract and calculated its value. Then, say that the risk-free interest rate increases during the contract period.
Why would that impact your option valuation?
That's it!
Not quite.
The value of an option is the present value of the expected future payoff, so the interest rate is an important part of the equation.
So it's definitely something to keep track of. And to do that, you'd be interested in finding __rho__. Rho is the change in a given portfolio for a given small change in the risk-free interest rate, holding everything else constant. It measures the sensitivity of the portfolio to the risk-free rate.
Think of a long call option. In that case, you'd purchase the call for stock exposure, with only a fraction of the total amount that it would have taken to purchase the same amount of shares. That difference could be invested in the risk-free rate. So for a call option, the rho is positive, and a higher interest rate increases the value.
But a long put is a different story. Why's that?
You got it!
When you enter a long put, the proceeds from the sale are delayed. For a put, rho is negative, so a higher interest rate lowers the put value.
When interest rates are zero, the call and put option values are the same for at-the-money options. That's because put-call parity indicates that the present value wouldn't have any impact on the valuation.
$$\displaystyle c - p = S_0 - e^{-rT}X$$
But in relation to volatility and changes in the stock, interest rates generally aren't a major concern.
No.
The premium is paid on a long put, so it's not interest received.
Not quite.
The long put is purchased, so the proceeds aren't received through the premium because that value's paid out.
To sum it up:
[[summary]]
The value is based on the present value of the expected payoff
The value is based on a deposit rate of the premium received
The premium acts as the interest rate
The proceeds from the sale are delayed
The proceeds are received through the premium
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