Important Stuff

Question 1

Black Scholes

Answer 1

log returns are normally distributed, constant sigma and r, no arbitrage, no transaction costs, no taxes, asset prices change continiously, cant jump

Question 2

Merton Model

Answer 2

BS with extension that volatility is time varying (volatility is a deterministic function of time, sigma in BS is defined as the average vol over the life of an option); risky bond = riskless bond - put

Question 3

Heston Model

Answer 3

BS with stochastic volatility

Heston Model with Jumps includes jump component

Question 4

Vasicek

Answer 4

Model of short term interest rate where interest rates are mean mean reverting and can become negative; not every yield curve is possible

Question 5

Hull-White

Answer 5

Model of short term interest rate where r is time varying and time-0 term structure is exactly matched, interest rates can become negative

Question 6

CIR Model

Answer 6

Model of short term r where volatility can increase with interest rate, r can NOT become negative

Question 7

Black-Karasinski model

Answer 7

F being monotonic function of short rate, r can NOT become negative

Question 8

Monte Carlo

Answer 8

Pricing based on simulation of outcomes of underlyings

Question 9

Brownian Motion

Answer 9

Mean zero with volatility suqareroot(delta t) and total variation infitiy, quadratic variation is T

Question 10

Geometric Brownian

Answer 10

Drift and sigma constant, drift in instand dt = mu dt

Question 11

Ito Process

Answer 11

Can be a geometric brownian motion but doesnt have to be as drift and sigma can be random, evolves continiously over time

Question 12

Blacks Formula

Answer 12

Black Scholes based on forward or future, dividend yield magically disappeard

Question 13

Cap and Floor

Answer 13

zerocoupon bond options, can be price in vasicek and hull white with blacks formula

Question 14

Swaption

Answer 14

Option on coupon bearing bonds

can be priced in vasicek and hull white with jamshidians trick