MS. Asrar Alyafie

Mathematics department

2nd Semester

2018

MS. Asrar Alyafie MATH 333

office # 308

office hours : 11-1 Sunday , Monday, Tuesday

email: aalyafeae@uj.edu.sahttp://www.uj.edu.sa/DRS-1001102.aspx

MS. Asrar Alyafie MATH 333

Assessments

H.W 20%

Test 1 20%

Test 2 20%

Final exam 40%

Text books:

• J. Hull, Options, Futures and Other Derivatives, 8th Edition, Prentice-Hall, 2008.

• P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press, 1995.

MS. Asrar Alyafie MATH 333

Introduction:

Elementary Economics Background.

Forward Contract.

Options.

MS. Asrar Alyafie MATH 333

This course is concerned with mathematical models for financial markets:

• Stock Market ( المالية" األسهم"سوق األوراق)" , Such as NYSE (New York Stock Exchange),

London stock exchange, Tokyo....

• Bond Market ( المالية" الضمانات"سوق السندات) , where participant buy and sell debit

securities.

• Futures and Option Markets (سوق الخيارات المالية والمستقبلية) , where derivative products

(المنتجات المشتقة) are traded.

Derivative: is a financial instrument “contract” whose value depends on the more basic

underlying variables ( the price of traded asset).

MS. Asrar Alyafie MATH 333

•Forward Contract (العقود اآلجلة) , it is a simple derivative. It is an agreement to

buy or sell an asset at a certain future date (expiration date or maturity يوم "

"اإلستحقاق T) for a certain price (the strike price ”سعر السوق“ K, exercise price

"سعر التنفيذ" E).

❖One of the parties to a forward contract assumes the long position and

agrees to buy the asset. The other party assumes a short position and agrees

to sell the asset.

MS. Asrar Alyafie MATH 333

Futures and forward contracts are agreements to buy or sell an asset at a

future time for a certain price.

Futures contracts are traded on an organized exchange, and the contract

terms are standardized by that exchange. By contrast, forward contracts are

private agreements between two financial institutions or between a financial

institution and one of its clients.

MS. Asrar Alyafie MATH 333

Example: Consider the forward contract which trade one share of asset in one year (T) for a price 1000$ (K)

The pay off(1):

Long position: S(T) –K

Short position: K- S(T)

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(1)The cash realized by the holder of a derivative at the end of its life.

MS. Asrar Alyafie MATH 333

•Call option C: gives the holder the right to buy the underlying asset for a certain price K at a certain date T.

•Put option P: gives the holder the right to sell the underlying asset for a certain price K at a certain date T.

•To close the option the investor has to do the opposite transaction.

MS. Asrar Alyafie MATH 333

OptionsCall

Put

MS. Asrar Alyafie MATH 333

Options:

American option can be exercised at any time up to the maturity

European option can be exercised only at maturity itself.

Option market is massive! More money is invested in options than in the

underlying securities. The main purpose of this course is to determine the fair

price of options.

Example: Call option

Consider the situation of an investor who buy a European call option with a strike price 1000$ to purchase one share. The current stock price 800$, the expiration date is one year and the price of an option to purchase one share (deposit, initial payment) is 100$.

The pay off from the call option: max (S(T)-K, 0)

If S(T) > K : S(T) –K

If S(T)< K : 0

MS. Asrar Alyafie MATH 333

Example: Put option

Consider the situation of an investor who has a European put option with a strike price 1000$ to purchase one share. The expiration date is one year and the price of an option to purchase one share (deposit, initial payment) is 100$.

The pay off from the put option: max (K-S(T), 0)

If S(T) > K : 0

If S(T)< K : K-S(T)

whereas the purchase of a call option is hoping the stock price will increase, the purchase of a put option is hoping that it will decrease.

MS. Asrar Alyafie MATH 333

H.W.

1. What is the difference between:a) a long position and a short position?

b) A call option and put option?

c) American option and an European option?

d) Forward contract and future contract?

2. The value of payoff under the situation of an investor who has a European put option with a strike price 800$ to purchase one share. The expiration date is one year and the price of an option to purchase one share is 1000$.

MS. Asrar Alyafie MATH 333