Options trading with profit discounting

Posts: 1
Joined: Wed Nov 06, 2013 9:24 am

Options trading with profit discounting

Postby monsieuruzairo3 » Wed Nov 06, 2013 9:27 am

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?
Choose one answer.
Choose one answer.
a. 9.5 Correct
b. 10 Incorrect
c. 9.29 Incorrect

My appraoch
The Profit is 10(115-105). However this is realized at the end of 18 months. So we need to discount it back to today.

Convert 4%(T=1) to continuously compounded rate = 3.92%
Since 18 month spot rate is not given so I will use (5%) and multiply by 0.5 Continoulsy compounded rate of 5% = 4.88%

Therefore discounting factor = exp(.0392*1) * exp(.0488*0.5) = 1.06566
Discounted profit = 10/1.06566=9.38 ~ 9.4
However answer is 9.5

Posts: 1
Joined: Fri Nov 15, 2013 7:52 am

Options trading with profit discounting

Postby deepali » Fri Nov 15, 2013 9:40 am

Value at end of t=18 months=max(St-105,0)-max(St-115,0)
105<St<115=>value=St-105 so max value=10
So max payoff that can occur in 18 months is 10.
Use discrete compounding it would had been given if continuous been used
Discounting factor would be (1+.04)^1*(1+.05/2)^.5=1.04*1.0124=1.0529
So discounted profit/payoff=10/1.0529=9.498~9.5

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