stock market    online trading
10 Yr. T-Note

(0.00%)
S&P 500

(0.00%)
NASDAQ

(0.00%)

When you buy stocks it is very important to understand lookback option.

Lookback option

PDF Print E-mail

The Lookback options are a type of exotic options with path dependency, among many other kind of options. The payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. The option allows the holder to "look back" over time to determine the payoff. There exist two kinds of Lookback options : with floating strike and with fix strike.

Lookback option with floating strike

As the name introduces it, the option's strike price is floating and determined at maturity. The floating strike is the optimal value of the underlying asset's price during the option life. The payoff is the maximum difference between the market asset's price at maturity and the floating strike. For the call, the strike price is fixed at the lowest asset's price of the option's life, and, for the put, it is fixed at the highest asset's price. Note that these options are not really options as there will be always exercised by their holder. In fact, the option is never out-of-the-money, which makes it more expensive than a standard option. The payoff functions are given by, respectively for the Lookback call and the Lookback put:

 

where Smax is the maximum asset's price during the life of the option, Smin is the minimum asset's price during the life of the option, and ST is the underlying asset's price at maturity T.

Lookback option with fixed strike

As for the standard European options, the option's strike price is fixed. The difference is that the option is not exercised at the price at maturity: the payoff is the maximum difference between the optimal underlying asset price and the strike. For the call option, the holder choose to exercise at the point when the underlying asset price is at its highest level. For the put option, the holder choose to exercise at the underlying asset's lowest price. The payoff functions are given by, respectively for the Lookback call and the Lookback put:

where S_{max} is the maximum asset's price during the life of the option, S_{min} is the minimum asset's price during the life of the option, and K is the strike price.

Arbitrage free price of Lookback options with floating strike

Using the Black-Scholes Model, and its notations, we can price the European Lookback options with floating strike. The pricing method is much more complicated than for the standard European options, and can be found in Musiela. Assume that there exists a continuously-compounded risk-free interest rate r>0 and a constant stock's volatility σ >0. Assume that the time to maturity is T>0, and that we will price the option at time t

Then, the price of the Lookback call option with floating strike is given by:

where

and where Φ is the standard normal cumulative distribution function,

Similarly, the price of the Lookback put option with floating strike is given by:

Arbitrage free price of Lookback options with fix strike

Using the Black-Scholes Model, and its notations, we can also price the European Lookback options with fix strike. Assuming the same as for the Lookback option with floating strike and using the same notations, the price at time t

If M < K

and if M>K,

The fact that there is two different prices depending on whether M is greater than K or not, can be explained by the following. If M > K , then the event  {Smax > K} is always true. This implies that the expected payoff function at time t is then Smax-K instead of \max(Smax-K,0).

Similarly, the price at time t

If m>K,

and if m<K


Lookback option Topic - Derivatives

A derivative is a financial instrument that is derived from some other asset, index, event, value or condition (known as the underlying asset). Rather than trade or exchange the underlying asset itself, derivative traders enter into an agreement to exchange cash or assets over time based on the underlying asset. A simple example is a futures contract: an agreement to exchange the underlying asset at a future date.


 
Home
Take me Home Mrs. Juno
About Juno
Want to know more about us?  How we started?  The People?
Advertising
Advertising Ideas? Feel free to click on Contact Us and tell us about it. We are not going to pollute our home page with your banner though.
Privacy Policy
We take your privacy extremely serious.

Online Trading Articles
General articles about online trading, stock brokers, stock trading and options trading.
Software
Take a look at all of the online trading and day trading software we have, true innovation at $4.95 a trade.
Contact Us
We are here to Help!
Help
We have a ton of questions already answered if you want to look yourself.

PLEASE READ THE IMPORTANT DISCLOSURES BELOW.

Securities products and services offered by Transcend Capital, LLC, a registered broker dealer, Member FINRA/SIPC.
6500 River Place Blvd., Bldg. 4, Ste. 102, Austin, TX 78730. 512-623-7774.

The information contained on this Web site does not constitute an offer to buy or sell, or the solicitation of an offer to buy or sell securities. No information found on this Web site should be construed by any consumer as investment advice, tax advice or a recommendation or solicitation to effect or attempt to effect transactions in securities.

Symbols and price and volume data shown here are for illustrative purposes only. Transcend Capital and/or its employees and/or officers may have positions in securities referenced herein, and may, as principal or agent, buy from or sell to clients. Account access, trade executions, and system response may be adversely affected by market conditions, quote delays, system performance, and other factors.

Any specific securities, or types of securities, used as examples are for demonstration purposes only. None of the information provided should be considered a recommendation or solicitation to invest in, or liquidate, a particular security or type of security.

Options carry a high level of risk and are not suitable for all investors. Please read the Options Disclosures Document Characteristics and Risks of Standardized Options before considering any option transaction

Certain requirements must be met to trade options at Transcend Capital. With long options, investors may lose 100% of funds invested. Multiple leg options strategies will involve multiple commissions. Spread trading must be done in a margin account. Please read the Options Disclosure Document titled Characteristics and Risks of Standardized Options before considering any option transaction.

Exchange, order-routing or other types of fees may increase or decrease the net cost of a particular trade. A listing of these fees can be found here ; other account-related fees may be found here.

Diversification and Asset Allocation strategies do not ensure a profit and cannot protect against losses in a declining market. While an investment in a specific sector may involve a greater degree of risk than an investment with greater diversification, strategies that include broadly diversified portfolios do not ensure a profit and do not protect against losses.

Additional advanced options education is available from the OIC.

Transcend Capital, LLC and JunoTrade Corporation are not legally affiliated.


stock market
User Name/Password do not match.
Please enter a Valid User Name and Password.
Forgot your Password?
Enter your Email Address in the form below and select 'Reset' and we will ask you to answer your Security Question before we Email a temporary password to you.

Email Address:

Forgot your Email Address?
Please call 1-800-284-8114 with you Account number and your personal information including the answer to your Security Question.