Question

9

(9) A $100 par value bond matures 1 bond. It pays par value at maturity. currently selling for So= $40 and in 6 months What is the value of a call option on the ue of a call option on the stock with strike price X=$45, where the call Puron pays max(ST-X, 0)? (Solve with whichever method you choose.) You will have to solve for the replicating portfolio first. alue bond matures in 6 months. (No coupon payments are made by the ar value at maturity.) Its discount rate is 6%. The stock of a company is 8 for So $40 and in 6 months will be selling for either Sr=$48 or S1-532

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Answer 1

Use Black Scholes Formula to calculate the price of call option which pays max

Spot price (Current Market Price) (SP) : $ 40

Strike Price (ST) : $ 45

Exponential constant (e)  = 2.7182818

Time to Expiration (t) : 6 months

Volatility When price is $ 48 after 6 months : ($ 48- $ 40) / $ 40 *100 = 20%

When price is $ 32 after 6 months ($ 32 - $ 40)/ $ 40 * 100 = 20%

So Volatility (σ) is 20 %

Interest Rate Risk Free (r) : 6%

Value of Call option is $ 0.96 (See Formula below)

C = SP * N(d₁) - ST * N(d₂)

Where, d₁ = ( ln(SP/ST) + (r + (σ²/2)) t ) / σ √t

d₂ = d₁ - σ √t

N (.) is the cumulative standard normal distribution function