Investment Theory and Risk Management, + Website

Pricing European Put Options

Let's take the same $1 stock and price a five-month put with strike price $0.90, implying that the put is currently in the money. The put option will have value max(K – S,0) at the terminal nodes as shown in Figure 16.11.

Figure 16.11 Five-Month Put Option Value

Again, I refer you to the Chapter 16 spreadsheet for specifics but the process is identical to call valuation, that is, we still work backward, discounting the weighted average of the relevant two front-running node values. Note that max for all but the two lowest spot prices in the fifth month. Because the exercise price is $0.90, then the spot price needs to be below this level for the put to have value. Valuation mechanics are otherwise the same as for call options. For example, at the penultimate node for the put for which the two possible terminal spot prices are $0.84 and $0.75, we get, for example:

We conclude that a five-month put on a $1 stock has value today equal to $0.01.