## option pricing quiz 2

Good Student
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Joined: Thu Oct 04, 2012 2:09 am

### option pricing quiz 2

A European-style call spread consists of a long position in the 105 strike call and a short position in the 115 strike call both maturing in 18 months. The options are on a stock index with an annualized dividend yield of 1% per annum. The interest rates are 4% (annual compounding) for 1 year and 5% (annual compounding) for 2 years. Under these circumstances, what is the number nearest the maximum value of this position today?
a. 9.5
b. 10
c. 9.29
d. 9.4
how to calculate?

content.pristine
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Joined: Wed Apr 11, 2012 11:26 am

### Re: option pricing quiz 2

This is a bull spread using calls.
Luckily, this question is not complicated by premiums in the question.
Now, the max profit happens when the the underlying rises beyond the higher strike price of call.
Hence, lets take a value of 120.
Payoff from first call = 120- 105 = 15
Payoff from second call = 115-120 = -5
Hence P&L = 10.

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swarnendupathak
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### Re: option pricing quiz 2

Thats fine... but this value is after 18 months..don't we need to discount it to today's date???

Swarnendu

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### Re: option pricing quiz 2

what are the use of values of interest rates and yield given in this question?

content.pristine
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### Re: option pricing quiz 2

Good Point Swarnendu.
Yes. This needs to be discounted.
Thanks for pointing that out!

swarnendupathak
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### Re: option pricing quiz 2

But to be discounted at what rate???? as we need to discount it for 18months & the rates are mentioned for 1 year & 2 years???? Please clarify

Swarnendu

content.pristine
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### Re: option pricing quiz 2

Since the we need the interest rate for 18 months, we need to interpolate.
The interest rate for 1 year + int rate for 6 months after that
1 dollar invested will give:
1*e^(0.04+0.025)=1.067159
You can directly use this as the denominator to discount.

swarnendupathak
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Thanks....