Futures and Options – The basics.

Option valuation: Method II (Part 2)

Option pricing – method II (Part 2)

The two stage binomial pricing was a simple method. In our example we assumed that the stock was trading Rs 100 and that in the next one year, the stock may move up 20% or fall 10%. We tried the value the European option that had a strike price of Rs 95 assuming the risk free rate was 12%. If we draw a picture, the price movement and pay off probabilities would have looked like this –


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Option Valuation: Method II (Part 1)


In the last post we discussed the risk neutral method of pricing options. In this post we would discuss binomial method of option pricing which, in reality, is just an extension of the risk neutral method.

BINOMIAL PRICING MODEL.

We will check out binomial model with the help of an example –

Let’s assume that the stock is trading Rs 100 right now. In the next one year, the stock may move up 20% or fall 10%.  European options are available at a strike price of Rs 95. What would be the value of a European call if the risk free interest rate is 12%?

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Option valuation – Method 1.

So far, from our earlier posts we learned –

  • The nature of option contracts
  • Factors that affect the valuation of option contracts
  • And, certain restrictions on upper and lower bound of options prices.

From this post onwards, we proceed to learn the methods of option pricing. The first point we would like to say is that, option valuation, however simple, requires a bit of mathematical calculations. The methods we would discuss in this series are:

  • Risk neutral model
  • Binomial model
  • And, The Nobel prize winning Black-Scholes model.

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Option valuation: Upper and lower bounds -Part III

We have already discussed the upper limits and lower limits of European options in our earlier posts. Now, here we discuss the remaining part – upper and lower limits of American options.

Upper bounds of American calls:

We know that an American call option can be exercised at any time during the contract period. The principle of upper bounds of american calls are the same as we saw in upper bounds of European call values. The difference in excersisability will not make any impact on the upper bound values .So, the upper bound value of an american call can never rise beyond the value of the underlying stock. When the dividend is known with certainty, the call values cannot rise beyond the spot value of the stock less present value of the dividend.It’s straight forward and needs no further explanation.

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