Question

In: Finance

The price of Swearengen, Inc., stock will be either $65 or $87 at the end of...

The price of Swearengen, Inc., stock will be either $65 or $87 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent.

  

a.

Suppose the current price of the company's stock is $76. What is the value of the call option if the exercise price is $61 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

  Call value $   

  

b.

Suppose the current price of the company's stock is $76. What is the value of the call option if the exercise price is $71 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

  Call value $   

Solutions

Expert Solution

a

Upmove (U)= High price/current price=87/76=1.1447
Down move (D)= Low price/current price=65/76=0.8553
Risk neutral probability for up move
q = (e^(risk free rate*time)-D)/(U-D)
=(e^(0.03*1)-0.8553)/(1.1447-0.8553)=0.60521
Call option payoff at high price (payoff H)
=Max(High price-strike price,0)
=Max(87-61,0)
=Max(26,0)
=26
Call option payoff at low price (Payoff L)
=Max(Low price-strike price,0)
=Max(65-61,0)
=Max(4,0)
=4
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)
=e^(-0.03*1)*(0.605207*26+(1-0.605207)*4)
=16.8

b

Upmove (U)= High price/current price=87/76=1.1447
Down move (D)= Low price/current price=65/76=0.8553
Risk neutral probability for up move
q = (e^(risk free rate*time)-D)/(U-D)
=(e^(0.03*1)-0.8553)/(1.1447-0.8553)=0.60521
Call option payoff at high price (payoff H)
=Max(High price-strike price,0)
=Max(87-71,0)
=Max(16,0)
=16
Call option payoff at low price (Payoff L)
=Max(Low price-strike price,0)
=Max(65-71,0)
=Max(-6,0)
=0
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)
=e^(-0.03*1)*(0.605207*16+(1-0.605207)*0)
=9.4

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