Valuation of Contingent Claims Flashcards
What does Δ represent in option
Delta: Change in the value of the option, for a change in underlying price
What is Δ hedging?
Taking an offsetting Δ postion so to be delta neutral
Δ = 0
Formula for Δ hedge
Δ Neutral = - Δ portfolio / Δ hedge
What is Γ in option
Γ: Gamma
Second derivative of Δ
The change in option Δ for a change in the underlying assets price
What does Γ measure
Measures the risk that remains once a portfolio is delta neutral
It can be managed to a specific level, but never eliminated
A portfolio that must be gamma neutral can become delta neutral by trading
The underlying securities.
What is θ in options
θ Theta
change in option value for the passage of time
estimates how much value slips away from an option with each passing day
Theta is the rate in which the time value decreases as time goes on
What will our θ be if we long options
Negative θ
Time is our enemy
What will our θ be if we short options
Positive θ
Option decay in value
What is ν in options
ν: vega
Change in option for change in volatility
How will our vega be if we long options?
Positive vega (Long volatility)
How will our vega be if we short options?
Negative Vega (Short volatility)
What is ρ in options
ρ: Rho
Change in option value for a change in the Risk Free Rate
What is Delta range for a call option at any moment in time
Non dividend: 0 to1
Dividend: 0 to e^(-δT)
What is the implied volatility in options based off of?
It is the volatility implied by the option prices observed in the market
What probability is N(d2) in the BSM?
probability the option expires in-the-money
With currency options, the volatility in the BSM model is the volatility of the log returns of…
The Spot exchange rates as expressed as Sd/f
What is the Stock component in the BSM
S x N(d1)
What is the Bond component in the BSM
e^(-r x T) X N(d2)
What is a Collar option strategy?
buying a downside put and selling an upside call to protect against large losses, but that also limits large upside gains.
Buy put, Sell call.
What is a straddle option strategy?
buying (or selling) both a call and a put with the same strike price and expiration on the same underlying asset.
Buy or sell put and call option witht he same stike and expiration
When does gamma at its highest value?
When the option is near, or at the money
What is the PV of expected option payoff at expiration in the BSM model?
- The PV is based on the Risk-free interest rate and not the investors required rate of return.
- The expected option payoff is based on the risk-neutral probabilities.
