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# Option Valuation Techniques

## Option Valuation Techniques

Option Valuation Techniques: The Value of an Option at Expiration Date: We have already been introduced to characteristics of both European and American Options. Assuming a European Call Option on a non dividend paying stock it is easy to see that its value at expiration date shall either be zero or the difference between the market price and the exercise price, whichever is higher. It may be noted that the value of an Option cannot be negative. An investor is required to pay a premium for acquiring such an Option. In case this premium is less than the value of the Option, the investor shall make profits, however, in case the premium paid is more than the value, the investor shall end up losing money. Note that, while measuring these gains or losses, Time Value of Money and  transaction Costs have been ignored.

Option Valuation Techniques

(a) Binomial Model: The binomial model breaks down the time to expiration into potentially a very large number of time intervals, or steps. This requires the use of probability and future discrete projections through which a tree of stock prices is initially produced working forward from the present to expiration.

To facilitate understanding we shall restrict ourselves to an European Option having a one year time branching process where at the end of the year there are only two possible values for the common stock. One is higher and the other lower than the current value. Assume that the probability of the two values to materialize is known. In such a situation a hedged position can be established by buying the stock and by writing Options. This shall help offset price movements. At each step it is assumed that the stock price will either move up or down. The pricing of the Options should be such that the return equals the risk free rate.

Option Valuation Techniques

At the end of the tree – i.e. at expiration of the option – all the terminal option prices for each of the final possible stock prices are known as they simply equal their intrinsic values.

(b) Risk Neutral Method: The “risk-neutral” technique can also be used to value derivative securities. It was developed by John Cox and Stephen Ross in 1976. The basic argument inthe risk neutral approach is that since the valuation of options is based on arbitrage and is therefore independent of risk preferences; one should be able to value options assuming any set of risk preferences and get the same answer as by using Binomial Model. This model is a simple model.

Option Valuation Techniques