Simulating Risk Neutral Stochastic Processes with a View to pricing Exotic Options
Simulating Risk Neutral Stochastic Processes with a View to pricing Exotic Options
Files
Publication or External Link
Date
2006-04-25
Authors
Kim, Sunhee
Advisor
Madan, Dilip
Fu, Michael
Fu, Michael
Citation
DRUM DOI
Abstract
Absence of arbitrage requires all claims to be priced as the
expected value of cash flows under a risk neutral measure on the
path space and every claim must be priced under the same measure.
This motivates why we want to use the same measure to price
vanilla options and path dependent products, and hence why we want
to match marginal distributions.
There are many ways of matching marginal distributions. We present
simulation methods for three stochastic processes that match
prespecified marginal distributions at any continuous time: the
Az\'{e}ma and Yor solution to the Skorohod embedding problem,
inhomogeneous Markov martingale processes with independent
increments using subordinated Brownian motion, and a continuous
martingale using Dupire's local volatility method. Then the
question is which way is a good way of matching marginal
distributions.
To make a judgement, we look at the properties of the processes.
Since all vanilla options are already matched, we want to use
exotic options to investigate properties of the processes. One of
the properties that we investigate is whether forward return
distributions are close to spot return distributions as market
structural features.
We price swaps associated with the first passage time to barrier
levels on these processes and see which model gives the highest
value of swaps, in other words, the shortest passage time to
levels. Moreover, we price monthly reset arithmetic cliquets with local
floors and global caps and with local caps and global floors. Then
we check the model risks of these models and find how model risks
change when caps or floors change. Finally, we price options on
the realized quadratic variations to see how option prices move as
maturity increases.