<p>Think about what happens 1 year from now.  You will deliver the stock and receive 90, either through the exercise of the call or the exercise of the put, depending on whether the then stock price is above or below 90.  So in the end you have spent 86.53 to get back 90 one year later.  Now you can calculate the risk free rate.  Note that no options model is required to prove this.  In quant lingo , put-call parity is a model free identity.</p>

CC BY-SA 4.0
2024-04-17T05:57:09.563Z
2024-04-17T05:57:09.563Z
dm63
<p>You buy a share of stock, write a 1-year call on the stock with strike price of $90,</p>
<p>and buy a 1-year put option with the same strike. The cost of this three-instrument</p>
<p>portfolio is $86.53. The stock pays no dividends.</p>
<p>What is the risk-free rate?</p>
<p>I'm assuming this is a european option but I can't use the binomial valuing methods or put call without making some serious assumptions. Any help appreciated?</p>

<asset-pricing>
Put Call Parity Question - Calculating Risk free rate ; has my professor left something out or is it possible?
Daragh McQuaid
# Put Call Parity Question - Calculating Risk free rate ; has my professor left something out or is it possible?

(Asked by: username_0 on 2024-04-16)

You buy a share of stock, write a 1-year call on the stock with strike price of $90,

and buy a 1-year put option with the same strike. The cost of this three-instrument

portfolio is $86.53. The stock pays no dividends.

What is the risk-free rate?

I'm assuming this is a european option but I can't use the binomial valuing methods or put call without making some serious assumptions. Any help appreciated?

**Tags:** asset-pricing


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## 1 answers

### Answer by username_1 on 2024-04-17. Score: 0

Think about what happens 1 year from now. You will deliver the stock and receive 90, either through the exercise of the call or the exercise of the put, depending on whether the then stock price is above or below 90. So in the end you have spent 86.53 to get back 90 one year later. Now you can calculate the risk free rate. Note that no options model is required to prove this. In quant lingo , put-call parity is a model free identity.


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