You buy 1000 six months ATM call options on a non-dividend paying asset with spo

Question

You buy 1000 six months ATM call options on a non-dividend paying asset with spot price 100, following a lognormal process with volatility 30%. Assume the interest rates are contant at 5%.

(a) How much do you pay for the options?

(b) What Delta-hedging position do you have to take?

(c) On the next trading day, the asset opens at 98. What is the value of your position (the option and shares position)?

(d) Had you not Delta-hedged, how much would you have lost due to the decrease in the price of the asset?

Please show all work for every part.

Explanation / Answer

a. since the options are ATM, delta is close to -0.5, and to delta-hedge the long put position we need to purchase 500 (0.5*1000) units of the underlying asset.

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