# Option Pricing Theory and Applications ## Option pricing model damodaran

= V - D if V D

= 5 if V

where,

V = Value of the firm

D = Face Value of the outstanding debt and other external claims

## Option Pricing Models - How to Use Different Option

The above-mentioned classification of options is extremely important because choosing between European-style or American-style options will affect our choice for the option pricing model.

### Option Pricing Model to Value a Product Patent or Option

Debt Type Face Value Duration

Short term Debt \$ 865 mil years

Bank Debt \$ 985 mil years

Senior Debt \$ 887 mil years

Senior Subordinated \$ 878 mil years

Total \$ 8555 mil years

#### Valuation Models | Valuation (Finance) | Option (Finance)

Illustration 6: Effects on equity of a conglomerate merger

You are provided information on two firms, which operate in unrelated businesses and hope to merge.

Firm A Firm B

Value of the firm \$655 million \$ 655 million

Face Value of Debt \$ 85 million \$ 55 million (Zero-coupon debt)

Maturity of debt 65 years 65 years

Std. Dev. in firm value 95 % 55 %

Correlation between firm

cashflows

The ten-year bond rate is 65%.

A formal definition of an option states that it is a type of contract between two parties that provides one party the right, but not the obligation, to buy or sell the underlying asset at a predetermined price before or at expiration day. There are two major types of options: calls and puts.

• Two ways to price options are the Black-Scholes model and the Binomial model. The Black-Scholes model is used to find to find a call price by using the current stock price, strike price, the volatility, risk free interest rate, and the time until the option expires. The Binomial model uses a tree of stock prices that is broken down into intervals. This tree represents the potential value of a stock from the present date and until the expiration. From this, one can find the value of the option with the strike price, volatility, risk free interest rate and the stock price at expiration date.

Assumptions
6. All the assumptions underlying the Black-Scholes model apply
7. The current value of the project and the variance in this value are known.

We generate the random number  ↋  and solve for S(T). Afterward, the process is similar to what we did for simulation in the binomial model: find the option’s payoff at the maturity and discount it to the present value.

Under the binomial model, we consider that the price of the underlying asset will either go up or down in the period. Given the possible prices of the underlying asset and the strike price of an option, we can calculate the payoff of the option under these scenarios, then discount these payoffs and find the value of that option as of today.

The simplest method to price the options is to use a binomial option pricing model. This model uses the assumption of perfectly efficient markets. Under this assumption, the model can price the option at each point of a specified time frame.