Problem 3. Probability for a call to be in the money at maturity (15 points) The

Question

Problem 3. Probability for a call to be in the money at maturity (15 points)

The stock of Network Communication Corp. (NCC) is currently traded at $50 on the market. Assume the stock price has a lognormal distribution. The expected return from the stock is 15 percent per annum and its volatility is 25 percent per annum. What is the probability that a European call option on NCC stock with a strike price of $52 and a maturity of 3 months will be in-the-money at the maturity date?

Please show each step broken down and show in word or excel

Explanation / Answer

Since the stock follows lognormal distribution, we can use Black-Scholas-Merton (BSM) Model of option valuation s to calculate probability for a call to be in the money at maturity.

In BSM model, N(d1) refers to probability of option ending in the money.

d1 = {ln(S0/X) + [(Rf+ (0.5 x 2)] x T} / { x T}

d1 = {ln(50/52) + [(0.15+ (0.5 x 0.252)] x 0.25} / {0.25 x 0.25}

= {-0.0392 + 0.0453} / 0.125

= 0.0488

Therefor N(d1) = N(0.0488) = 0.52

(Using z from Normal distribution table)

Therefore probability that a European call option on NCC stock with a strike price of $52 and a maturity of 3 months will be in-the-money at the maturity date is 0.52

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