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....

...Markets
FI 4200/AFM
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 time before or at expiration.
A European Option can be exercised only at expiration
- There are always two positions in an option contract:
BUYER and SELLER.
The buyer of an option has to pay a “price”, the so-called option premium. The seller of an option receives the option premium.
The option premium is an immediate expense for the buyer and an immediate return for the seller, whether or not the owner (=buyer) ever
exercises the option
- Four basic positions in options:
(1) Buying a Call à Long Call
(2) Selling a Call à Short Call
(3) Buying a Put à Long Put
(4) Selling a Put à Short Put
Buyer (Long)
Seller (Short)
Put
- Obligation to deliver the
underlying, if buyer
exercises the option
- Pays the premium
Call
- Right to buy the underlying
(i.e. to exercise the...

...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 part a. Again use the risk-neutral method to value this call option, but this time do not work back recursively. Rather, focus on the terminal distribution of stock price (and the number of paths which lead to each terminal stock price). Assume a European-style put option is written on this stock. It has 8 months to expiry and a $25 strike price. Focusing on the terminal distribution of stock price, value this put option.
Question 2
[European v. American Put Option]
A stock is currently priced at $100. In any given 3-month period, stock price will either go up by 13.31% or down by 11.75%. The riskless rate of interest is 5% per annum continuously compounded. A put option is written on this stock with a $110 strike price and 9 months to expiry. a) b) c) Assume the put option is European-style. Calculate the current value of the put. Use whatever method you like, but it will be quickest to focus on the...

...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
No-arbitrage pricing
Understanding Risk Neutral Valuation
3
Arbitrage (Definition)
• An arbitrage opportunity is one which:
a.Requires no invested capital
b.Provides a positive profit with 100% probability
• Or (slightly more generally)
a.Requires no invested capital,
b.Provides a positive profit with a positive probability and
has a zero probability of a loss.
• Anyone who prefers more to less would engage in arbitrage
because it represents “something for nothing”
• Therefore: in any competitive market there should be no
arbitrage
Understanding Risk Neutral Valuation
4
“No-Arbitrage Pricing”
• Although absence of arbitrage is simply a necessary
requirement for equilibrium it is in some cases sufficient to
allow us to price one security in terms of another
• Idea: assets / portfolios with the same cash flows in each
state must have the same price
• Pricing via no-arbitrage is relative pricing: we calculate
the price on one security in terms of the prices of...

...
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 exchange-traded and, therefore, are regularize contracts. Forward reduce, on the other part, are private agreements between two partly and are not as unmitigated in their stated expression and qualification. Because forward incur are private agreements, there is always a chance that a party may failure on its side of the agreement. Futures confine have clearing hotel that guarantee the transactions, which drastically diminish the likeliness of default to almost never.
Secondly, the particular details participation settlement and deliverance are quite conspicuous. For forward contracts, arrangement of the shorten occurs at the close of the reduce. Futures contracts are conspicuous-to-offer diurnal, which means that daily alter are regulate Time by age until the destruction of the contract. Furthermore, pacification for futures confine can happen over a range of dates. Forward contracts, on the other ability, only possess one dregs misdate.
Lastly, because futures contracts are perfectly often...

...Hussein 900061146
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 value of a business decision that a manager has an option, or right, but not an obligation to fulfill.
Basically, there are two types of real options Growth and Flexibility. Growth options help the company to increase its future business such as in the research and development, brand development, leasing or developing land, mergers and acquisitions and most important initiating a new technology. Flexibility options are different as they give the firm the ability to change its plan in the future and adapt to a new one. For example, the company may want to buy the option to delay, expand, contract, switch uses, outsource or abandon projects.
Real options are considered powerful analytical tools as they capture the value of managerial flexibility to adapt decisions that would help to take an action towards any unexpected market developments. Companies associate their investment...

...general market conditions. This phenomenon allows the investor to have higher profits and higher losses if the transaction is not developed as I thought.
The value of the derivative changes in response to changes in the price of the underlying asset. Currently there are derivatives on all asset classes such as currencies, commodities, stocks, stock indices, precious metals, etc.
Derivatives can be traded both organized stock exchanges or organized or not also called counter markets.
Like any 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 previously authorized. Furthermore, both the exercise price and the maturity of the contracts are the same for all participants. The operations are performed on an exchange or regulated and organized center such as the Chicago Mercantile Exchange in the United States, where he traded derivatives and futures contracts.
Derivatives contracted in unorganized or OTC markets: These are derivatives whose contracts and specifications are tailored to suit the parties to the derivative contract. In these...

...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 Mercantile Exchange (CME) opens International Monetary Market (IMM) CME began with grain and commodities future contracts more than a hundred years ago.
7.1.2 The International Monetary Market (IMM) provides:
a) An outlet for hedging currency risk with future contracts (* explanation of hedging next page)
b) Definition of future contracts (above)
c) Main available futures currencies
* EUR (Euro) - CHF (Swiss Franc)
* GBP (Britain Pound) - BRL (Brazilian Real)
* CAD (Canadian Dollar) - AUD (Australian Dollar)
* JPY (Japanese Yen) - NZD (New Zealand Dollar)
d) Standard contract sizes contract sizes differ for each of the available currencies. For example:
EUR = 125.000
GBP = 62.500
e) Transaction costs : payment of commission to a trader
f) Leverage is high the initial margin is required is relatively low, for example, less than 0, 2% of sterling contract value)
g) Minimum price movements contracts set to a...

...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 exercised, IBM issues more stock
7. Which of the following is not true?
a. Futures contracts nearly always last longer than forward contracts
8. In the corn futures contract a number of different types of corn can be delivered (with price adjustments specified by the exchange) and there are a number of different delivery locations. Which of the following is true?
b. This flexibility tends decrease the futures price.
9. Which of the following is true?
b. The principal amounts usually flow in the opposite direction to interest payments at the beginning of a currency swap and in the same direction as interest payments at the end of the swap.
10. A trader sells 10 call option contracts on a certain stock. The option price is $10, the stock price is $50, and the option’s delta is 0.65. How can the trader hedge the short position so that the portfolio is delta-neutral?
b. The trader needs to buy 650 shares. 0.65 * (-10)*100 = - 650. buy 650 shares to create a delta-neutral position....