## Sleepless in LA Case Solution

**Option Pricing Framework**

The option pricing framework is used to calculate the fair values of the options. The most common models that are used to value options are the binomial model and the Black Scholes model. This option given the holder a right and not any obligation to either sell or purchase the underlying commodity at the specified price at a future date.

**Valuing Corporate Equity and Risky Debt using Option Pricing Framework**

The option pricing framework and the option pricing models can also be used to value the corporate equity and the risky debts of the corporations. For instance, when any company issues debt to the public, it means that the company is selling the asset to the lenders. However, on the other hand an option is obtained by the shareholders of the company and this option lets them to buy back the assets of the company by simply paying all the lenders all the outstanding amount at the time of the debt maturity. This option is basically a call option which is purchased by the shareholders of the company over the assets of the company.

Therefore, in a similar way, the corporate equity could also be valued using the option pricing theory. The bondholders and the stockholders have differing objectives and these different objectives usually lead towards the agency problems and this conflict could be easily demonstrated using the option pricing framework. There are five key inputs that are required in order to value equity and risky debt through options.

The first one is the risk free rate, the second component is the volatility or the standard deviation of assets if debt is to be valued and the standard deviation of assets is used if the debt is to be valued. The third variable is the time to maturity. The fourth and the fifth components are the price of the underlying asset and the exercise prices. If there are any changes in these five key inputs the prices of debt and equity calculated through the models would differ significantly. For instance, if the time to maturity is increased then the value of the put and the call option also increases. Therefore, all the key inputs impact upon the value of the corporate equity and risky debt.

**Valuing Options through Black Scholes Model**

There are two types of options which are the American and the European options. The European options are priced using the Black Scholes model. The basic difference between both of these option types is that the European options could not be exercised before the expiry date. As defined above there are five key variables on the basis of which the price of the options is determined. One of the core component is the volatility which is the fluctuation of the stock returns of the underlying asset or the company.

If the standard deviation of the return is higher, then the premium calculated through the Black Scholes model would also be higher. Along with this the stock price of the option is one of the critical variable which is impacted by many internal and external factors of the company. If we look in exhibit 3, then there are various prices of call and put options offered at a range of exercise prices and maturities in June, September and December.

The calculations have been performed in the excel spreadsheet to calculate the call and the put option prices based on the inputs provided in exhibit 3. The prices for the call and the put options have been created for a range of excursive prices as show in exhibit 3. However, when we compare the price for the call options and the put options with the market prices as provided in exhibit 3 then it has been noticed that the prices are not similar and there is insignificant difference between the market prices and the prices of the call the put options calculated using the Black Scholes model.

The difference in prices is not caused due to any error but there are some important explanations for the difference in the prices. For instance, the demand and supply in the market has strong impact upon the prices of the options. For instance, if the investors have the view that the stock price of a particular company would appreciate in future then they are more likely to purchase an out option over the stocks of that company. This means that the demand for the options increases and as a result the prices of the options are also increased in market value terms whereas the prices calculated through the models differs..........................

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