Perpetual American Options; Introduction
to Exotic Options
1 Perpetual American Options
2 Introduction to Exotic Options
3 Asian Options
Perpetual American Options; Introduction
to Exotic Options
1 Perpetual American Options
2 Introduction to Exotic Optio
On Market-Making and Delta-Hedging
1 Market Makers
2 Market-Making and Bond-Pricing
On Market-Making and Delta-Hedging
1 Market Makers
2 Market-Making and Bond-Pricing
What to market makers do?
Provide immediacy by standing ready to sell to buyers (at as
HW: 5
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 5
Its lemma. Exchange rates as GBM. Sharpe ratio.
o
Provide your nal answer to the following problem(s):
Problem 5.1. Let Z = cfw_Z(t), t 0 b
HW: 7
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 4
University of Texas at Austin
HW Assignment 7
Sharpe ratio. Risk-neutral probability measure. Black-Scholes pricing. Stock-price powers.
Provide your nal answer to the following problem
HW: 6
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 3
University of Texas at Austin
HW Assignment 6
Sharpe ratio. Risk-neutral probability measure. Black-Scholes PDE. Black-Scholes formula.
Provide your complete solution to the following p
HW: 6
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 6
Sharpe ratio. Risk-neutral probability measure. Black-Scholes PDE. Black-Scholes formula.
Provide your complete solution to the following p
HW: 7
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 7
Sharpe ratio. Risk-neutral probability measure. Black-Scholes pricing. Stock-price powers.
Provide your nal answer to the following problem
HW: 8
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 8
The Black-Scholes model. Power forwards. Correlated assets.
Arithmetic stock-price average. Option Greeks.
Provide your nal answer only to
Option Greeks
1 Introduction
Option Greeks
1 Introduction
Set-up
Assignment: Read Section 12.3 from McDonald.
We want to look at the option prices dynamically.
Question: What happens with the option price if one of the inputs
(parameters) changes?
Fir
mama A awe: 53.86% a " " " K
_ "n
' . . geéumm QAvqu-e V A f" 37. The price of a stock is governed by the stochastic differential equation: W
't
. dsm _ _ _ (o.03- 9:3.) .t
W _ 9:.9'3dr +92de0), .) 3 (+3 - awe a.
3 (+0 ssco) em -t + 0220:.)
where {Z(t)}
More Exotic Options
1 Barrier Options
2 Compound Options
3 Gap Options
More Exotic Options
1 Barrier Options
2 Compound Options
3 Gap Options
Denition; Some types
The payo of a Barrier option is path dependent
More precisely, the payo depends on whether
More on Market-Making and
Delta-Hedging
What do market makers do to
delta-hedge?
Recall that the delta-hedging strategy consists of selling one option,
and buying a certain number shares
An example of Delta hedging for 2 days (daily rebalancing and
Day
HW: 9
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 1
University of Texas at Austin
HW Assignment 9
Power forwards. Forward start options. Rolling insurance strategy.
Arithmetic stock-price average. Option Greeks.
Provide your nal answer o
Quiz: 5
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 1
University of Texas at Austin
Quiz # 5
Black-Scholes pricing formula
Please, provide a complete solution to the following problem(s):
Problem 5.1. Consider a continuous-dividend-payin