**Please explain/show how my professor got the following answers to our study guide questions. **

1. Consider a European-style Call option on a stock (that pays no dividends). The following parameters apply: Initial Stock Price: $92; Exercise Price: $90; Risk-free rate per period: 4.5%; Option matures at end of one period and over that one-period the stock will either go up by 19% or go down by 14%.

(a) Using a one-period Binomial Option Pricing Model to price this Call, what is the fair theoretical price for this European-style call option today?

ANSWER: p(RNP) = 0.561; Cu=19.48; Cd=0; C=$10.45

2. Consider an AMERICAN-style PUT option on a stock (that pays no dividends). The following parameters apply: Initial Stock Price: $61.25; Exercise Price: $65; Risk-free rate per period: 5.0% Option matures at the end of the second period (T=2 periods). Over each of the two periods, the stock will either go up with an up-factor u of 1.24 or go down with a down-factor d of 0.84.

(a) Using a two-period binomial option model, what is the fair theoretical price for this PUT option today?

ANSWER: Pu2 = 0; Pud = $1.202; Pd2=$21.78; p(RNP) = 0.525 Then: Pu(model)=0.544; Pu(IV) = 0; so Pu=0.544 Pd(model)=10.45; Pd(IV)=13.55; so Pd=13.55; Then Put(American-style) = $6.40

b) What if the above Put option instead had been a European-style option?

ANSWER: Different, using model-implied values for Pu and Pd=> Put(European) = $5.00