question archive The current price of a stock is Rs 40 and the continuously compounded risk-free r = 8%
The current price of a stock is Rs 40 and the continuously compounded risk-free r = 8%
Subject:FinancePrice:2.86 Bought7
The current price of a stock is Rs 40 and the continuously compounded risk-free r = 8%. You sold a 40-strike call
with 3 months to expiration at a premium Rs 2.78 and at the same time you bought a 40-strike call with 1 year
to expiration for a premium Rs 6.28. The theta for the long call is -0.0104 and that for the short call is -0.0173.
Find the profit once the sold option has expired, if the stock price remains at Rs 40 and nothing else has changed.
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Rs 1.1088
Step-by-step explanation
Profit = Premium earned from short call - Premium lost on long call
As stock expired at strike price we can earn full premium which is Rs. 2.78 Because value of the premium became Rs. 0 on expiry.
So, there is decline of Rs.2.78 in 3-months at the theta (measure of decay) -0.0173
For long call theta is -0.0104
So, Decay in premium on long call = 2.78 * (-0.0104/-0.0173) = 1.6712
Profit = 2.78 - 1.6712 = Rs 1.1088
