Essay About Daily Prices And Original Asian Option Example

Operations Management
Solution to Homework Problem Set #4
Decision Models & Optimization Page 1 Term II, 2016
1. Trusty BankCo’s Lookback Option
a) Model the payoff calculation for a simulation that prices the lookback option.
Like the original Asian option example, the element of uncertainty here is the daily return
over each of twenty days. The daily prices and final payoff are functions of these
random variables.
Data and Variables:
time index: t = 0, 1, 2 … , 20
Random Variables for daily returns: Rt, t =1, 2, …, 20
where each Rt is normally distributed with mean 0.0% and std dev 1.84%.
Other notation: daily prices: Pt, t=0, 1, … , 20
where P0 = $60.00 and Pt = Pt-1 (1+Rt).
Expression for the payoff calculated at the end of the month:
average price: Pavg = 1/20 (P1 + P2 + … + P20)
minimum price: Pmin = min{P1, P2 , … , P20}
payoff = Pavg – Pmin
b) Evaluate the simulation results.
Figure 1 displays how the Asian option spreadsheet model can be modified to model the
“lookback” option. The frequency chart and summary statistics for the simulation
experiment are also shown below.
Solution to Homework Problem Set #4
Decision Models & Optimization Page 2 Term II, 2016
Figure 1: Spreadsheet for Lookback Option