Intrinsic and Time Value
intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price – exercise price for a put option: exercise price – stock price

the intrinsic value for out-the-money or at-themoney options is equal to 0 time value of an option = difference between actual call price and intrinsic value as time approaches expiration date, time value goes to zero 21-2

Determinants of Option Values
Call + – + + + – Put – + + + – +

Stock price Exercise price Volatility of stock price Time to expiration Interest rate Dividend rate of stock

21-3

Binomial Option Pricing
consider a stock that currently sells at S0 the price an either increase by a factor u or fall by a factor d (probabilities are irrelevant) consider a call with exercise price X such that dS0 < X < uS0 hence, the evolution of the price and of the call option value is uS0 Cu = (uS0 – X) C S0 dS0 Cd = 0 21-4

Binomial Option Pricing (cont.)
now, consider the payoff from writing one call option and buying H shares of the stock, where Cu − Cd uS0 − X H= = uS0 − dS0 uS 0 − dS0 the value of this investment at expiration is Up Down Payoff of stock HuS0 HdS0 Payoff of calls –(uS0 – X) 0 Total payoff HdS0 HdS0 21-5

Binomial Option Pricing (cont.)
hence, we obtained a risk-free investment with end value HdS0 arbitrage argument: the current value of this investment should be equal to its present discounted value using the risk-free rate H is called the hedge ratio (the ratio of the range of call option payoffs and the range of the stock price) the argument is based on perfect hedging, or replication (the payoff of the investment replicates a risk-free bond) 21-6

Binomial Option Pricing – Algorithm
1. given the end of period stock prices, uS0 and dS0, calculate the payoffs of the call option, Cu and Cd 2. find the hedge ratio H = (Cu – Cd)/(uS0 – dS0) 3....

...Characteristics of Options
r Definitions and Positions:
- A Call Option gives its owner for a specified time the right to purchase an underlying good at a specified price (= exercise price or
strike price)
- A Put Option gives its owner for a specified time the right to sell an
underlying good at a specified price (= exercise/strike price)
- An American Option permits the owner to exercise (=buy/sell the
underlying) at any...

...Risk-Neutral
Valuation
Stephen M Schaefer
London Business School
March, 2012
Outline
• The no-arbitrage principle
• Arrow-Debreu (A-D) securities and market
completeness
• Valuing options with one period to maturity via
replication using underlying asset and borrowing /
lending
replication using A-D securities
risk neutral probabilities
• Valuing options with several periods to maturity
Understanding Risk Neutral Valuation
2...

...compounded. A European-style call option is written on this stock with a $12 strike price and 8 months to expiry. a) b) c) d) Use the delta-hedging approach to price this call option. Use the risk-neutral valuation method to price this call option. Work recursively back through the Binomial tree, calculating the call option price at each node. Check that the option price at each node matches that calculated in...

...
Forward, Futures, & Options
Heather L. Dirgo
BUS450: International Finance
Instructor Kristian Morales
September 29, 2014
Forward, Futures, & Options
Fundamentally, forward and futures abridge have the same function: each symbol of contracts allow people to buy or sell a particular type of asset at a particular time at a given price. However, it is in the specific details that these contracts differ.
First, futures contracts are...

...Introduction:
Real option analysis (ROA) is a decision-making structure that basically calculates the value of a future business decision. ROA borrows from financial options theory. A financial option gives the buyer of a financial asset the right, but not the obligation, to buy a stock or bond, for example, at a predetermined price at a future date. By analogy, a real option is a managerial decision-making tool that calculates the...

...contract, the derivatives are settled at a future date.
Role of Financial Derivatives.
We can classify financial derivatives based on different parameters. The most common are:
1. Derivatives according to the type of contract involved:
a. Options.
b. Forwards.
c. Contracts for difference.
d. SWAPS.
2. Depending on where derivatives are traded and traded:
Derivatives traded on organized markets: Here are standardized contracts on underlying assets that were...

...CHAPTER 7: CURRENCY FUTURES AND OPTION MARKETS
7.1 FUTURE CONTRACTS
7.1.1 Definition of future contract–> contracts written requiring a standard quantity of an available currency at a fixed exchange rate and at a set delivery date.
A future contract is defined as a contractual agreement to buy or sell an asset at a pre-determined price in the future. The contracts detail the quality and quantity of the underlying asset.
Background of currency futures in 1972: Chicago...

...following are always positively related to the price of a European call option on a stock?
c. The volatility
5. When we talked about Vega hedging, if a portfolio has 1000 shares of SPY and 10 contracts of at-the-money December 2013 put option on SPY (and nothing else in the portfolio), is the portfolio vega neutral?
c. No, the portfolio can never be vega neutral.
6. Which of the following is not true?
a. When a CBOE option on IBM is...