Derivation and Application of the Black free essay sample

Since the option confers on its holders a right with no obligation it has some value. Conversely, the writer of the option must be compensated for the obligation he assumed. The right to sell an asset in a put option and has payoff properties which are opposite to those of a call. A put option allows its holder to sell the asset on a certain date for a prescribed amount. The writer is then obliged to buy the asset. The holder of a call option wants the asset price to rise, the higher the asset price at expiry, the greater the profit. Whereas, the holder of a put option wants the asset price to fall as low as possible. An American option is one that may be exercised at any time prior to expiry. The options that can only be exercised at expiry are called European. In this project, I will only focus on the European type of options. We will write a custom essay sample on Derivation and Application of the Black or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 1. 3 Some economic definitions There are some important definitions need to be clarified besides the definition of an option. Definition 1 (Portfolio) A portfolio in finance is any collection of financial assets such as stocks, bonds and cash. 5 Definition 2 (Arbitrage) Arbitrage indicates that it is possible in a financial market to make risk-free profits larger than just placing money in the bank. Definition 3 (Derivative) A derivative instrument is a contract between two parties that specifies conditions (especially the dates, resulting values of the underlying variables, and notional amounts) under which payments, or payoffs, are to be made between the parties. Definition 4 (Arbitrage-free) If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium or arbitrage-free market. Definition 5 (Risk-free interest rate) The risk-free interest rate, r(t), is the growth rate of the real money supply, M, in very long time period. Definition 6 (Hedging) Hedging is a risk management strategy used to limiting or offset probability of loss from fluctuations in the prices of commodities, currencies, or securities. Definition 7 (Volatility) Volatility (? ) is related to the standard deviation of the stock price of a share. It is an indication of some random behavior of the market. 6 1. 4 List of symbols In order to stick with specific symbols throughout