30. What is the value of a 3-month put with a strike price of $45 given the Blac

Question

30. What is the value of a 3-month put with a strike price of $45 given the Black-Scholes Option Pricing Model and the following information? Stock price Exercise price $46 $45 Time to expiration 25 Risk-free rate 3-month 45 call 065 $4.96 31·The assets of Bill's Boats are currently worth $47,600. These assets are expected to be worth either $45,000 or $53,000 one year from now. The company has a pure discount bond outstanding with a $50,000 face value and a maturity date of one year. The risk-free rate is 4 percent. What is the value of the equity in this firm? (Round your answer to the nearest whole dollar.)

Explanation / Answer

30)

using put-call parity

P = C + X*EXP(-r*T) - S

   = 4.96 + 45*EXP(-0.065*0.25) - 46

   = 3.23

31)

Call when asset is 45000 = Max(0,45000-50000) = 0

Call when asset is 53000 = Max(0,53000-50000) = 3000

number of call option = (53000-45000) / (3000 - 0) = 2.667

Now

47600 = 2.667*C + 50000/(1+4%)

2.667*C = 4330.769

C = 1624 = equity value

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