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You are given the following information concerning a stock denoted by St (1) Current value =102. (2) Annual volatility =

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You are given the following information concerning a stock denoted by St
(1) Current value =102.
(2) Annual volatility = 30%.
(3) You are also given the spot rate r = 50%, which is known to constant during the next 3 months
It is hoped that the dynamic behavior of St can be approximated reasonably well by a binomial process if one assumes observation intervals of length 1 month
(a) Consider a European call option written on St. the call has a strike price K = 120 and expiration of 3 months. Using St and the risk-free borrowing and lending, Bi, construct a portfolio that replicates the option.
(b) Using the replicating portfolio price this call
(c) Suppose you sell, over-the-counter, 100 such calls to your customers. How would you hedge this position? Be precise.
(d) Suppose the market price of this call is 5. How would you form an arbitrage portfolio?

 Strike Price
In finance, the strike price of an option is the fixed price at which the owner of the option can buy, or sell, the underlying security or commodity. Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...

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a While the terminal values for the call option are 12 26 0 0 0 The hedging portfolio one should use …View the full answer


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An Introduction to the Mathematics of financial Derivatives

An Introduction to the Mathematics of financial Derivatives

ISBN: 978-0123846822

2nd Edition

Authors: Salih N. Neftci

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Question Posted: August 17, 2011 10:22:44
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Related Video

A call option is a type of financial contract that gives the holder the right, but not the obligation, to buy an underlying asset (such as a stock, commodity, or currency) at a specified price (called the strike price) within a specified period of time. When an investor purchases a call option, they are essentially betting that the price of the underlying asset will rise above the strike price before the option\'s expiration date. If the price of the asset does rise above the strike price, the investor can exercise the option by buying the asset at the strike price and then selling it at the higher market price, thereby earning a profit. Call options are often used as a speculative investment strategy, as they allow investors to potentially profit from the upward movement of an asset without having to actually own the asset itself. They are also commonly used as a hedging tool to protect against potential losses in a portfolio.

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