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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)
stock price at T=1 if price goes up
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)
Repos and Reverse Repos.
the process of adjusting hedge ratios to maintain a riskless portfolio
feature of binomial model
can accommodate the early exercise feature of american options
T:F --> no arbitrage arguments and risk-neutral valuation give the same answer
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
A long position in X shares of the stock and a short position in one call option. We can calculate X.
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