Question

Consider a stock currently trading at 25 that can go up or down by 15 percent per period. The risk-free rate is 10 percent. Use one-period binomial model. a. Determine the two possible stock prices for the next period. b. Determine the intrinsic values at expiration of a European call with an exercise price of 25. c. Find the value of the option today. d. Construct a hedge by combining a position in stock with a position in the call. Calculate the hedge ratio and show that the return on the hedge portfolio is the risk-free rate regardless of the outcome, assuming that the call trading at the price obtained in part c. e. Determine the rate of return from a risk-free hedge if the call is trading at 3.50 when the hedge is initiated. ***I really just need help with Part E. PLEASE SHOW ALL WORK.

Answer 1

a.) for A part we will use bionomial-tree approach as u will be 1.15, d will be .85

b.) & c.)

Template - Black-Scholes Option Value
Input Data
Stock Price now (P)		25
Exercise Price of Option (EX)		25
Number of periods to Exercise in years (t)		1
Compounded Risk-Free Interest Rate (rf)		10.00%
Standard Deviation (annualized s)		15.00%
Output Data
Present Value of Exercise Price (PV(EX))		22.6209
s*t^.5		0.1500
d1		0.7417
d2		0.5917
Delta N(d1) Normal Cumulative Density Function		0.7709
Bank Loan N(d2)*PV(EX)		16.3541
Value of Call		2.9173
Value of Put		0.5382

d..)

Hedge ratio = Spot price/future price or resent value as per the formula

1.105170918

E)

Change if the theoritical call is 3.5.

Template - Black-Scholes Option Value
Input Data
Stock Price now (P)		25
Exercise Price of Option (EX)		25
Number of periods to Exercise in years (t)		1
Compounded Risk-Free Interest Rate (rf)		13.45%
Standard Deviation (annualized s)		15.00%
Output Data
Present Value of Exercise Price (PV(EX))		21.8536
s*t^.5		0.1500
d1		0.9717
d2		0.8217
Delta N(d1) Normal Cumulative Density Function		0.8344
Bank Loan N(d2)*PV(EX)		17.3602
Value of Call		3.5000
Value of Put		0.3536

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