Pricing and Hedging with Monte Carlo Simulation

Simulation

 Project

  Pricing

 and

 Hedging

 with

 Monte

 Carlo

 Simulation

Yun

 Jin

  149000585

  Abstract:

  This

  paper

  attempts

  to

  implement

  Monte

  Carlo

  simulations

  in

  order

  to

  price

  and

  hedge

  options.

  Many

  options

  have

  no

  analytic

  solutions.

  Given

  the

  strong

  assumptions

  of

  the

  Black-­‐Scholes

  world,

  after

  a

  review

  of

  the

  literature,

  we

  analyze

  via

  simulations

  the

  impact

  of

  stochastic

  volatility

  on

  the

  valuation

  of

  Asian

  and

  European

  options;

  next

  we

  examine

  how

  the

  various

  hedge

  weights

  perform

 in

 the

 case

 of

 a

 European

 call

 on

 a

 basic

 Black-­‐Scholes

 asset.

  1

 Pricing

 options:

 a

 simulation

 approach

  My

  pricing

  method

  approach

  is

  based

  on

  Monte

  Carlo

  simulation;

  firstly

  I

  provide

  the

  central

  assumptions

  of

  the

  Black-­‐Scholes

  environment.

  Then

  detail

  the

 Monte

 Carlo

 simulation

 to

 pricing

 options.

  The

  Monte

  Carlo

  approach

  is

  an

  efficient

  application

  of

  the

  option

  pricing

  theory

  as

  summarized

  as

  followings:

  firstly

  simulating

  a

  path

  of

  the

  underlying

  asset

  under

  the

  risk

  neutrality

  condition

  ,

  then

  we

  need

  to

  discount

  the

  payoff

  corresponding

  to

  the

  path

  at

  the

  risk-­‐free

  interest

  rate,

  after

  repeating

  the...