Put-Call Parity SOA-type Questions
1. Consider a European call option and a European put option on a nondividend-paying
stock. You are given:
(i) The current price of the stock is 40.
(ii) The call option currently sells for 0.10 more than the put option.
Monte Carlo Valuation
Nuclear weapons and casinos
Monte Carlo valuation provides a solution to options/derivatives that cannot be priced with simple,
Monte Carlo valuation is performed using the risk-neutral distrib
Interest Rate and Bond Derivatives
A.k.a. fixed income derivatives
Derivatives with payoffs depending on bond prices or interest rates.
Why study these derivatives separately?
Introduction to Interest Rate Derivatives
Key: Derivatives w
Market-Making and Delta-Hedging
At least as important as the Black-Scholes formula is the Black-Scholes technique
What do Market-Makers do?
A market-maker stands ready to sell to buyers and to buy from sellers supply immediacy,
The Lognormal Distribution
Probability theory and more
It is common in option pricing to assume the lognormality of asset pricesbut why?
foundation for extension
The Normal Distribution
Normal distribution: tw
Historical and implied volatilities
Volatility is a critical input for option price but cannot be directly observed. In the class we focus
on two topics (both mentioned in previous lectures):
Implied volatility information o
The Black-Scholes-Merton Equation
Revisit the market-maker problem with Itos Lemma
Differential Equations and Valuing under Certainty
Black and Scholes derive a PDE which describes the price of an optionthe methodology of using
Do not let the name deceive you
XYZ Corp., a U.S. based corporation with sizable European operations.
Thus has a large monthly inflow of euros that will be converted to dollars at the end of each
If this is an American Option, use the number "1"
If this is an European Option, use the number "0"
If this is an American Option, use capital letter "A"
If this is an European Option, use capital letter "E"
Brownian Motion and It
Heuristic understanding of stochastic processes
Stock and other asset prices are commonly assumed to follow a geometric Brownian motion.
Characterize the stochastic process of an option from