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Consider another example to calculate the annualized ordinary rate of return over a five-year period of an investment that returns 10% p.a. for two of the five years and -3% p.a. for the other three. The ordinary time-weighted return over the five-year period is:
Here the price of the option is its discounted expected value; see risk neutrality and rational pricing. The technique applied then, is (1) to generate a large number of possible, but random, price paths for the underlying (or underlyings) via simulation, and (2) to then calculate the associated exercise value (i.e. "payoff") of the option for ...
The modified Dietz method [1] [2] [3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the ...
For example, suppose a call option with a strike price of $100 for DEF stock is sold at $1.00 and a call option for DEF with a strike price of $110 is purchased for $0.50, and at the option's expiration the price of the stock or index is less than the short call strike price of $100, then the return generated for this position is:
Price of the underlying: Any fluctuation in the price of the underlying stock/index/commodity obviously has the largest effect on the premium of an option contract. An increase in the underlying price increases the premium of call options and decreases the premium of put options. The reverse is true when the underlying price decreases.
In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option. [4]
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