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In finance, the binomial options pricing model ( BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" ( lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting.
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. [ 1] It is calculated by using the following formula: where. is the return in scenario ; is the probability for the ...
Risk-neutral measure. In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to ...
Option time value. In finance, the time value ( TV) ( extrinsic or instrumental value) of an option is the premium a rational investor would pay over its current exercise value ( intrinsic value ), based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market ...
This is a return of US$20,000 divided by US$100,000, which equals 20 percent. The US$20,000 is paid in 5 irregularly-timed installments of US$4,000, with no reinvestment, over a 5-year period, and with no information provided about the timing of the installments. The rate of return is 4,000 / 100,000 = 4% per year.
Merton's portfolio problem. Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.
Stock B is trading at a forward P/E of 30 and expected to grow at 25%. The PEG ratio for Stock A is 75% (15/20) and for Stock B is 120% (30/25). According to the PEG ratio, Stock A is a better purchase because it has a lower PEG ratio, or in other words, its future earnings growth can be purchased for a lower relative price than that of Stock B.
If the price was greater than $350 we would not purchase the information, if the price was less than $350 we would purchase the information. If the price was exactly $350, then our decision is futile. Suppose the price for the information was $349.99 and we purchased it. Then we would expect to make 1030 - 349.99 = 680.01 > 680.
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