# Category Archives: OPTION VALUATION

## SUMMARY

SUMMARY > Options are a special type of financial contracts under which the buyers of the options have the right to buy or sell the shares/stocks hut do not haw obligation to do so. > Essentially, options are of two types: call and put. A call option gives the holder the right, but not the obligation to buy specified stocks at a specified price! (known as the exercise price) on or before a specified mat

## Application of BS Model

Application of BS Model The solution of BS formula requires five variables. Out of these 5 variables, the four variables, namely, E, R, T and S are easily observable/known to market participants. The only unknown variable is the standard deviation of the share price, its value can be determined by referring to weekly observations of the share prices in the immediate preceding year; this value of standard devia

## Assumptions

Assumptions The BS model is based on the following assumptions (1) It considers only those options which can be exercised at their maturity that is, European options. (2) The market is efficient and there are no transaction costs and taxes. Options and shares arc infinitely divisible. Information is available to all investors with no costs. (3) The risk-free rate or interest rate are known and constant during the

## The BS Formula

The BS Formula Pricing of an option requires building a portfolio in shares and a loan in such a manner that its payoffs are equivalent to the payoffs from the option. We also know that there are five factors which influence the value of option: current share price, exercise price, risk free rate of interest, time to expiration on the option and price volatility of share (measured in terms of variance), The BS

## THE BLACK-SCHOLES OPTION PRICING MODEL (Table)

TABLE Payoffs With Purchase of 2/3 Share With Borrowings THE BLACK-SCHOLES OPTION PRICING MODEL Since both alternatives yield identical payoffs. both investments today must have the same value to avoid arbitrage (explained earlier). C  = Value of 2/3 of a share - Borrowings = Rs 100 - Rs 81.82 = Rs 18.18. The call option should sell at Rs 18.18. The net cost of buying the option equivalent (Price of 2/3rd sha

## THE BLACK-SCHOLES OPTION PRICING MODEL

THE BLACK-SCHOLES OPTION PRICING MODEL Black and Scholes (BS) developed a precise model to arrive at the equilibrium value, of an option. Before the BS mood is discussed in detail. it will be useful to understand the concept of option equivalent. The concept involves the purchase of a certain number of equity shares (say /\ shares) through, the partial sum raised by debt, This combination should be such that th

## Assigning Probabilities (Example)

EXAMPLE An investor is considering all option on the two shares, X and Y. Details are as follows. Assigning Probabilities The expected value of share price at the end of the period is the same for both shares, X and Y: Rs 120. There is a much larger dispersion of possible outcomes for share Y (the range being Rs 60 - Rs 180) vis-a-vis share X (the range of price variation is Rs 90 - Rs 180, Suppose the exercise

## Assigning Probabilities

Assigning Probabilities Hitherto volatility in share prices has been explained without assigning any probability. The induction of an element of probability would provide more insight into the matter.

## Price Volatility of Share

Price Volatility of Share Volatility in the share price influences the call option value. In operational terms, the greater is the possibility of extreme outcomes, the greater is the call option value to its holder, all other things remaining that is. In statistical terms, the greater is the variance/standard deviation of the financial returns on it associated share, the more is the worth of the option to its ow

## Time to Expiration/Maturity (Table)

TABLE Value of Investment at Year-end 1 (i) When Shares are Purchased and (ii) when Call Options are Purchased In Conjunction with Treasury Bills. Time to Expiration/Maturity Since both the alternatives have exactly the same value in the future, they should have the same value today; otherwise, difference in value gives rise to arbitrage. The value of call option (C) should be: So = 4/3 C + (Rs 140/1 + R) Rs 1