Equity and Interest Models Flashcards
What is the drift term of a stochastic process vs volatility term
dt term if drift
Volatility term includes a random process
What is the long run mean of a mean reversion process
alpha(mean-Xt)dt
What is meant by markov process - how to spot
Process is markov process is it only depends on the current value of Xt
What is meant by a stationary process - how to spot
Not stationary means no mean reversion
What processes have discontinuous paths
Gamma, poisson
What can be said about continuity for levy processes
Continuous in probability - not necessarily in paths except for BM
What Levy processes have in relation to quadratic variation
Finite variation
Things to check visually for stochastic process
Can it be negative,
Continuous? Increasing?
Quadratic variation finite? or deterministic for Weiner
Jumps or continuous? What happens at the limits?
Mean reversion and stationarity?
Long run mean
Variability how it varies
Markovian?
Martingale ? no dt term?
For what does the BSPDE have to hold
For any path independent self financing portfolio, it must hold. Holds in the region where the option isn’t worth its intrinsic value
What happens with propotionality and BSPDE solutions
If we find a solution to BSPDE bounded solutions are proportional to it by contant of the value on the exercise boundary
What is delta
Differential price wert S
What is gamma mathemtaically
2nd differential wrt S
What is theta mathematically
Differential price wrt t
How to see if two instruments agree on a barrier
Sub in st=Barrier to value formula
What is the terminal boundary condition vs boundary condition
Terminal boundary condition is condition on expiry : when is option worthless basically and where is the option value defined in terms of T and S
Knock out option value
Vanilla option - Knock in option
What are the conditions for deflator
Must ahve Deflated cash accoutn and deflated total return share protfolio be martingales - ir no dt term.
What si the ultimate forward rate - meaning
The rate towards which the extrapolation of the yield curve converges beyond the Last Liquid Point (LLP)
Explain why the construction of a risk netural law is less of a computational simplification for interest rate models compared to equity models with deterministic interest rates.
For RN model with inetrest deterministic deflator is deterministic. Cash flow valuation reduces to discounting the expected cash flow at initial RF rate. With stochastic interest rates, the deflator is RV so the valuation requires the calculation of an expected product
What is a self financing portfolio?
One where no purchases except from reinvested inetrest and dividens and no sales except to pay interest on borrowings or divs on short positions
What type of process underpins black scholes
GBM
What does path independent mean
Portfolio value V is a function of t and of the share price St but not of the path of the share price before time t
What are dirichlet conditions
They are boundary conditions that fix the limiting value f a solution at the boundary fo a domain
What are the boundary conditions for an upper known-out barrier H
On price boundary S=H t<T we have Value=0
On time boundary t=T we have for S<H value is given by option payoff
What are the boundary conditions for an lower known-out barrier H
On price boundary S=H t<T>H value is given by option payoff</T>
Can american option values be solved
No only approximated. There is no known analytical solutions for the prices of american options under BS
How good is binomial lattice method
Way to solve BSPDE by discretising the partial differential equation numerically. As a numerical method its not very efficient - convergence is quite slow as time step goes down to zero.
What is vega of the option
Sensitivity of the option price wrt volatility sigma
What the convention when calculating theta
Partial derivative wrt passage of time t , is the negative of the partial derivative wrt the outstanding term T-t to find theta
Whats the relationship between puts and calls for volatility
Implied volatility should be the same for same strike and term. Follows from put call parity
What is risk netural law
When by construction we use Lamda = 0
Carry cost
r-q
Risk premium
Lamda*sigma
In continuous paths inetrest rate process what will a positive shock to Wr do?
Downward shock to r but shall lead to an upward shock in bond prices
Risk neutral drift
=Real world drift +lamda*sigma
What are the consequences of setting lamda to 0 in the interest rate models
Risk neutral drift=Original real drift
Deflator is equal to reciprocal of cash account
Projections are unrealistic: have to work backwards by calibrating the model to market prices of bonds since we cant work with he drift
F=Deflator is still stochastic process - DIFFERENT TO EQUITY
Why can i set lamda to 0 int he interest rate models
It has no effect on bond of option prices
What si bonds boundary conditions
P(r,T,T) =1
What features should forecasting models have for interest rates?
Range of yield curve shapes
Parts of yield curve move separately
Discrete short rates
Multiple yield curves
None exploding rates
Interest rates lower bound
What are the criteria for bond option pricing models
Absense of arbitrage
Closed-form expressions for ZCB price
Closed-form expressions for options on bonds, ressembling BS for equity options
Ability to fit an arbitrary initial yield curve
Ability to fit observed market prices of options on bonds
Realistic dynamics
