Binomial Tree and Option Pricing

Calculating the value of Call and Put options using no arbitrage valuation

A stock’s price S is $100.After six months,it either goes up and gets multiplied by the up factor U = 1.16,or it goesdown and gets multiplied by the down factor D = 0. Options mature after T = 0.5 years and have a strike price K = 110.The continuously com- pounded interest rate is 5% for all maturities.

-Calculate the value of the call option using no arbitrage valuation.

-Demonstratehow you could make arbitrage profits when a trader quotes a call price of $2.

-Calculatethe value of the call option using risk-neutral  

-Calculate the value of the put option using no arbitrage valuation. 

-Demonstratehow you could make arbitrage profits when a trader quotes a put price of $12. 

-Calculatethe value of the put option using risk-neutral  

-Show the values of call and put options in (c) and (f) satisfy the put-call.

A firm has a debt of 5 million dollars with four months The firm does not pay coupon before the debt maturity. This firm has1 million outstanding number of shares with price being 3 dollars per share. The continuously compounded interest rate is 3% per annum. The volatility of firm value is 40%. Answer the following questions. The firm does not pay any dividend. 

-How much is the firm value? 

Hint: you could use solver add-in in the Excel to find the solution for a non-linear 

-What is the yield to maturity of the debt? 

-The firm proposes to the debt investors to restructure the debt by con- verting them into If you are an debt investor, what is the fair conversion ratio you will accept? 

a. Binomial Tree and option pricing

-Value of call option using no arbitrage valuation

SO=100 u=1.16 d=0.86 K=110 rf=0.05 t=0.5

(i) Su= SO * u = 100 * 1.16 = $116,Sd = so* d = 100 * 0.86 = $86

(ii)Payoff - Su-K= 116 -110 = 6-Sd- 0

(iii) Find the ?: 116?-6 = 86 ?,,? =(6/(116-86) = 0.2 Riskless portfolio is long 0.2 shares short 6 call option

iv) The value of the portfolio in 6 months is 116?-6 = 116(0.2) -6 = 17.2

v) Today profile PV = 17.2EXP(-0.05*0.5) = 16.77533

vi) Value of each share = SO *? = 100 *0.2 = 20

vii) Value of call option = value of share – today’s profile PV = 20 – 16.7753 = 3.22467.