In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or
down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time
step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein
parameterization to find the risk neutral probability and hence find the value of a European put
option with strike 102, given that the underlying price is currently 100.
C
A 2-step binomial tree is used to value an American put option with strike 105, given that the
underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10
and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying
and the continuously compounded risk free interest rate over each time step is 1%. What is the value
of the option in this model?
A
In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or
down by a factor of . The continuously compounded risk free interest rate over each time step is 1%
and there are no dividends paid on the underlying. The risk neutral probability for an up move is:
D
A 2-step binomial tree is used to value an American put option with strike 104, given that the
underlying price is currently 100. At each step the underlying price can move up by 20% or down by
20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the
underlying and the discretely compounded risk free interest rate over each time step is 2%. What is
the value of the option in this model?
C
Variance reduction is:
D
The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is
D
The gradient of a smooth function is
A
The Newton-Raphson method
B
What is a Hessian?
C
The bisection method can be used for solving f(x)=0 for a unique solution of x, when
A