## Options trading with profit discounting

monsieuruzairo3
Posts: 1
Joined: Wed Nov 06, 2013 9:24 am

### Options trading with profit discounting

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 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

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

### Options trading with profit discounting

Value at end of t=18 months=max(St-105,0)-max(St-115,0)
@St>115=>value=St-105-(St-115)=10
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