# Binomial Tree And Option Pricing

## Calculating Call and Put Option Values ​​Without Arbitrage Valuation

The price S of one share is \$100. After 6 months, it goes up and is multiplied by an upward factor U = 1.16 or down and is multiplied by a downward factor D = 0. The option expires in T = 0.5 years and has a strike price of K = 110. The perpetual interest rate is 5% for all maturities.

>>Calculate call option values ​​without arbitrage evaluation.

>>Shows how a trader can profit from arbitrage if the call price he quotes is \$2.

>>Calculate the value of call options in a risk-neutral way

>>Calculate put option value without arbitrage valuation. – Shows how to profit from arbitrage if a trader quotes a put price of \$12.

>>Calculate put option values ​​in a risk-neutral way

Display the call that satisfies the put call and the value of the put option in (c) and (f). A company has \$5 million in debt with a four-month term. The company will not pay the coupon until the debt is due. This company holds 1 million shares of his outstanding stock at \$3 per share. Continuous compound interest is 3% per annum. The volatility of enterprise value is 40%. Please answer the following questions. The company does not pay dividends.

―What is corporate value?

Note: You can find solutions for nonlinear solutions using the Solver add-in for Excel.

-What is the yield of the bond to maturity?

-The Company is proposing to bond investors to convert and restructure their debt. If you were a fixed income investor, what fair exchange ratio would you accept?

a. Binomial Trees and Options Pricing

Call option value without arbitrage evaluation 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) Payout – Su-K= 116 -110 = 6-Sd-0

(iii) find ?: 116?-6 = 86 ?,,? =(6/(116-86) = 0.2 risk free portfolio long, 0.2 shares short, 6 call options

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

v) Today’s Profile PV = 17.2EXP(-0.05*0.5) = 16.77533

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

vii) Call Option Value = Equity Value – Today’s Profile PV = 20 – 16.7753 = 3.22467.

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