"Compound interest is the eighth wonder of the world. He who understands it, earns it... he who doesn't, pays it." - Albert Einstein

Binomial Option Pricing is a method of determining the value, or premium to be paid, on a financial option contract such as a call or a put. This method of valuation relies exclusively on discrete interest calculation, as opposed to continuous interest calculation. The arithmetic differentiation of the two concepts is detailed in the table below, but an explanation is really quite simple. Imagine that you are playing a game of tag, and that you are it. The object of the game is to tag another player, thus making them it. While running, how would you try to gauge where the other players were escaping to? If you focus on just one other player, watch their every step, and make your own steps accordingly in a fashion to guarantee capture of the other player you have been making a continuous observation (and, most likely, are no longer it!). If you focus on just one other player, but keep your eyes closed, only opening them for a split second once every minute to see where the other player is, you have been making a discrete observation (and, most likely, will be it until everybody else goes home).

When referring to the time value of money, we may also apply an interest rate to our investment or borrowed principle using either discrete or continuous math. Continuous interest rates gain interest, and interest upon interest, constantly. Discrete interest rates gain interest (and interest upon interest) only at intervals defined when signing the contract to acquire funding at the given interest rate.

In general - one dollar today is worth more than a dollar tomorrow, and conversely is worth less than the same dollar yesterday. In specific - exactly how much more is an issue of fine-print, formal/acquired banking education, and scenario-relevant need.

t = time, generally noted in years, or fractions thereof
F0 = Value of asset at t=T, agreed upon at t=0
Q = Quantity of asset to be delivered at t=T, agreed to at t=0
S0 = Price of the asset at t=0
St = Price of the asset at t=t
e = The natural number, e
r = The interest rate for the contract period specified at t=0
s = The cost of storage, expressed as a percentage of the S0 at t=0
c = The convenience factor, economized, expressed as a percentage of the S0 at t=0
d = Any dividend, or leasing rate, expressed as a percentage of the S0 at t=0

Future Position Payoff Profit
Long (St - F0) * Q (St - F0) * Q
Short (F0 - St) * Q (F0 - St) * Q

interest compounding Valuation method
Discrete Binomial Option Pricing
Continuous Black-Scholes

McDonald, Robert L. "Derivatives Markets". 2006. Pearson Education, Inc.
TVM equations

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