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Level 123

Binomial Option Pricing Model


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Assumption for binomial options pricing
arbitrage opporitunities do not exhist (no-arbitrage pricing)
what does "h" represent
number of shares necessary to hedge a short position in one call option (sensitivity of the option price to movements in underlying stock)
Sd
stock price at T=1 if price goes up
p
population proportion
risk nuetral valuation
approach that allows us to assume investors are risk-neutral when we value derivatives (expect return on all assets to equal risk free rate)
R
Repos and Reverse Repos.
dynamic hedging
the process of adjusting hedge ratios to maintain a riskless portfolio
feature of binomial model
can accommodate the early exercise feature of american options
True
T:F --> no arbitrage arguments and risk-neutral valuation give the same answer
Delta
The rate of change of option value with respect to changes in the underlying asset's price. The first derivative of the value V of the option with respect to the underlying instrument's price S. Practic…
When is the portfolio riskless?
the portfolio is riskless when
Riskless portfolio
A long position in X shares of the stock and a short position in one call option. We can calculate X.
No-arbitrage argument
If there are two portfolios with the same initial cost, and they pay out exactly the same amount at the same time, they must have the same value.
— if he undervalues the portfolio, we will buy it from him
What do we do if we have a portfolio valuation and somebody else has a different valuation?
What is the value of the option?
the value of the option is therefore 5.000 − 4.367 = 0.633
— the value of the portfolio at time T is S0u*delta − fu
How do we introduce the notion of probability into up and down movements, where f is the price of a derivative at a certain time?
How do we interpret the variables p and (1 − p)?
the variables p and (1 − p) can be interpreted as the
What is the value of a derivative?
the value of a derivative is its expected payoff in a
Risk neutral derivative valuation
p*fu + (1 − p)fd = f*e^rT
Risk-neutral valuation principle
assume that the world is risk-neutral and calculate the price
American options vs European options
Work back through the tree from the end
Calculate P
pu+(1−p)d= e^r∆t