Question

Options are particularly difficult to understand. Put and call values are determined by the price of a stock, and yet you do not need to own the stock to buy a put or a call on that stock. In addition, if you buy a put or a call, you have the right to walk away from a contract to limit your losses. When you compute the price of an option, you use two models that are difficult to understand and have computations that are particularly challenging. what are some of the challenges you face in this scenario? How do you overcome them?

Answer 1

Although there are several options to calculate the price of the option (or most popularly known as the Theoretical Fair Value of the Option). For Instance, Expected Gain Approach, Price Differential Approach, Binomial Model, Black Scholes. But the latter two are the most commonly known and used for the purpose of calculating the price of the option. And also out of these two, Binomial also suffers from some of the challenges, making it difficult to use.

Under the binomial model, price of the option has been computed firstly, by assuming that the price of the share can either increase to some extent or decrease to some extent. For instance, current market price as well as strike price of a share is Rs 50. Now suppose it can move up either to Rs 60 (S1 say) or to Rs 40 (S2 say). Now we will calculate the value of option at both the prices S1 and S2, i.e. C1=10 (Max of (60-50,0)), and C2=0 (Max of (40-50,0)). Based on that we will calculate hedge ratio, [(C1-C2)/(S1-S2)]=0.5. Assuming that we can make fractional purchases, we will borrow an amount based upon the ratio of 0.5, and considering the market rate of Interest say 12%. So borrowing would be [0.5*{40/1.12}]=Rs 17.85. Fair Value of Call Option would be [(0.5*50)-17.86]=Rs 7.15.Thus, the calculation made considers the impact of both increase as well as decrease on the price of the share.

But some of its assumptions that portfolio value being maintained at the same level. And suppose the probability in the above mentioned example that chances of price increases are 90% and that of decrease would be 10%. No such use of such information is made in this model. And also this method believes that there are only 2 options available to investor to chose amongst, i.e. Rs 60 and Rs 40. Due to these assumptions, this method is quiet lesser used.

Black Scholes model, however overcomes some of its limitations like that, under this method consideration has been made to consider multiple levels, which got restricted only to 2 levels in the binomial model.

But it has its own assumptions like that there are no taxes in transaction cost, shares do not pay any kind of dividend during the option period, short selling being permitted and that too without any penalty, share prices moving randomly in continuous time.

Due to all such assumptions, makes it difficult to work in practical situations.

We can overcome such by using other model like GARCH Model, which is although not perfect but overcomes some of its limitations. We can also make use of several strategies like strangle, straddle, butterflies etc, in order to prevent loss from option trading.