Using a one period binomial model Given S0 = $20 K = $21 Su = $22 Sd = $18 r = 1

Question

Using a one period binomial model

Given

S0 = $20

K = $21

Su = $22

Sd = $18

r = 12%

T = 3 months

And e-rT

1. Draw a time line, solve for u and d, and draw the corresponding stock price tree.

2. Using the present value of the expected cash flows find the current value of the call option that expires in 3 months.

3. Using the present value of the expected cash flows find the current value of the put option that expires in 3 months.

4. Solve for delta, .

Where = [u u + d d] e-rT

= (u d )/(o( ))

u = (r*t )/( )

d = (1 u )

Using a two period binomial model

Given the information from above and the following:

t = .125 And

e^(-rt)

1. Draw a time line and draw the corresponding stock price tree.

2. Using the present value of the expected cash flows find the current value of the call option that expires in 3 months.

3. Using the present value of the expected cash flows find the current value of the put option that expires in 3 months.

Where

= [u u + d d] ^()

= (u d )/(0( ) )

u = (^() )/()

d = (1 u)

Explanation / Answer

S0 20 Su 22 Sd 18 Up move factor =22/20 1.1 Down move factor =18/20 0.9 0.13 0.2 Probability of Up Move =((1+r)-D)/(U-D) 0.65 * I have used discreet compounding here, meaning not used e^(r%*time), however the result would remain the same. 0.65 Probability of down Move =1-UP move 0.35 Binomial Tree Call Strike Call Profit in future 22 21 1 20 18 21 0 Call Payoff =Probability of Up move * Call value/(1+interest Rate for 3 months) =0.65*1/(1+12%/4) 0.631068 1 Binomial Tree Call Strike Call Profit in future Timeline 0 3 months 22 21 1 20 18 21 0 (please note, call option expires worthless here) 2 Call Payoff =Probability of Up move * Call value/(1+interest Rate for 3 months) =0.65*1/(1+12%/4) 0.631068 Call Payoff =Probability of Up move * Call value/(1+interest Rate for 3 months) =0.65*1/(1+12%/4) 0.631068 3 Binomial Tree Put Strike Put Profit in future Timeline 0 3 months 22 21 0 (please note, put option expires worthless here) 20 18 21 3 Put Payoff =Probability of Down move * Put value/(1+interest Rate for 3 months) =0.35*3/(1+12%/4) 1.019417

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