Views
2 years ago

Monotonicity of the stochastic discount factor and expected option ...

Monotonicity of the stochastic discount factor and expected option ...

To compute

To compute the variance, we first show thatCov (p (j) , p (i)) = − 1 V ar (p (j)) i ≠ j, i, j ∈ {1, . . . , k} .k − 1This is done by defining the random variable⎧⎪⎨ p (i) with probability (k − 1) /kx =⎪⎩ p (j) with probability 1/kNote that x is uniformly distributed on {1, . . . , k} and is independent of p (j).ThereforeUsing V ar (L t ) = V ar0 = Cov (p (j) , x) = k − 1k Cov (p (j) , p (i)) + 1 V ar (p (j)) .k(k∑jX j), we compute the variance:j=1V ar( k∑j=1jX j)=k∑j=1k∑ijCov (p (j) , p (i))i=1{ k∑= V ar (p (1))j=1⎧⎨ k∑= V ar (p (1))⎩j=1= V ar (p (1)) k2 (k + 1)12j 2 − 1k − 1j 2 − 1k − 1}k∑ ∑ijj=1i≠j⎛[ k∑] 2⎝ j − ∑j=1j⎞⎫⎬j 2 ⎠⎭Finally substituteV ar (p (1)) = 1 kk∑j=1(j − k + 1 ) 2= 1 (k + 1) (k − 1) ,2 1237

where we have used, for any k ∈ {1, 2, . . .},k∑j 2 =j=1k (k + 1) (2k + 1).638

Stochastic Discount Factors and Real Options - Annual International ...
Valuation Theory: Stochastic Discount Factor Stochastic Discount ...
Estimating the Stochastic Discount Factor without a ... - Economics
the Functional Stochastic Discount Factor - MIT
Stochastic Discount Factor Approach to International Risk-Sharing ...
Pricing Kernels and Stochastic Discount Factors - University of North ...
A Stochastic Discount Factor Approach to Asset Pricing Using Panel ...
Nonparametric Stochastic Discount Factor Decomposition - EPGE/FGV
Econometric specification of stochastic discount factor models.pdf
Latent Variable Models for Stochastic Discount Factors
Pricing Stock Options under Stochastic Volatility - SOM Research ...
The Present Value Model with Stochastic Discount Rate and an ...
Pricing Currency Options Under Stochastic Volatility
Why Do Firms With Diversification Discounts Have Higher Expected ...
Option Prices with Stochastic Interest Rates – Black/Scholes and Ho ...
Option Prices with Stochastic Interest Rates – Black/Scholes and Ho ...