Exotic Option Valuation Project

Exotic Option Valuation Project

Due at the beginning of class on November 8, 2017

        The goal of this project is to learn to apply two common numerical techniques, backwards induction on recombining binomial tree (BI), and Monte-Carlo simulation (MC), to valuation and parameter sensitivity analysis of two exotic derivative contracts.  Each contract will be paired with the valuation method in order to illustrate strengths and weaknesses of each method.  As you will learn in this project, BI method is easier to apply to contracts with early exercise features, while MC is easier to apply to contracts where payout depends on the price path of the underlying.  For this project you will be divided into eight groups of four and a pair of exotic options will be assigned to each group at random from the following set:

• Bermudan up-and-out exercise right option (BI), European knock-out-knock-in barrier option (MC)
• Bermudan down-and-out barrier option (BI), European knock-out-knock-in barrier option (MC)
• Bermudan game option (BI), European look-back option (MC)
• Bermudan reoption (BI), European Asian option (MC)
• Bermudan up-and-out exercise right option (BI), European cumulative Parisian option (MC)
• Bermudan up-and-out exercise right option (BI), European cumulative Parisian option (MC)
• Bermudan game option (BI), European Asian option (MC)
• Bermudan reoption (BI), European look-back option (MC)

The features of each of the above options contract will be covered in detail during the lecture.  A quick summary of the features is presented below:

Bermudan -- similar to American option in that it can be exercised before the expiration, however instead of being able to exercise it at any time, the buyer of the option may only do so at particular points in time on a set schedule, e.g. the option may be exercisable once a day at the close or once a month on a particular day.

Up-and-out exercise right -- the call (put) option may not be exercised early if the price of the underlying exceeds (falls below) a predetermined level.  The option can still be exercised at expiration if profitable to the options buyer.

Knock-out-knock-in barrier -- the call (put) option is null and void if the price of the underlying falls below (rises above) a predetermined level, set below (above) the strike price, however may become active again if the underlying consequently rises above (falls below) another predetermined level, set above (below) the strike price.

Down-and-out barrier -- the call (put) option is null and void if the price of the underlying falls below (rises above) a predetermined level, set below (above) the strike price.