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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