As shown in this chapter, Merton (1973) shows that for the case of an asset with price
Question:
As shown in this chapter, Merton (1973) shows that for the case of an asset with price S paying a continuously compounded dividend yield k , this leads to the following call option pricing formula:C = Se?kTN(d1) ? Xe?rTN(d2),where
a. Modify the BSCall and BSPut functions defined in this chapter to fit the Merton model.
b. Use the function to price an at-the-money option on an index whose current price is S = 1500, when the option?s maturity T = 1, the dividend yield is k = 2.2%, its standard deviation ? = 20%, and the interest rate r = 7%.
In(S/ X)+(r-k+o?/2)T d = oVT dz = d, -oVT
Step by Step Answer:
a Heres how we can modify the BSCall and BSPut functions defined in the chapter to fit the Merton mo...View the full answer
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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