check the book "global derivatives: prodcuts, theory and practice" - post-bgm you get smile/skew extensions of either SR or BGM

<r>replacement:First you need to understand the standard deviation of the population and the standard deviation of the mean estimate from a random sample (standard error) are different - I'm not sure which one you actually refer to in your reply to Aaron;Second the mean and the standard deviation de...

<t>Normally BEI are in the nominal/real bond context so no wonder you will find "BE swap rate". However in practice BEI and ZCIS can be interchangeable as ZCIS (0,T) is the market implied inflation-T. There will be slight differences though as BEI is derived and stripped from the coupon bonds, and b...

<t>Even for one-day var you don't calculate it as c*sd as the underlying Normality assumption is too naive. You have to take into account the tail behaviour.For 10-day var you need to study the rolling 10-day PnL vs. the underlying risk factors.However, given the exact one-day var but no further inf...

<t>Google the following two papers:A methodology to stress correlations: RiskMetrics® Monitor 4th Quarter 1997Correlation stress testing for value-at-risk: S Turkay, E Epperlein & N Christofides, Journal of Risk, Volume 5/4, Summer 2003Alternatively you can try the "pseudo inversion" as in the S...

<t>Depending on your purpose you can even use the initial yield curve as the input to the H-W model (to determine the instantaneous forward rate at future time t). However, as far as know, there are two government bond markets (exchange-based and inter-bank) in China so you need to sort out which ma...

shouldn't the risky asset be dS(t)/S(t) = R(t)dt, or (R(t) - y)dt, if y is for the deterministic dividend yield?For more details, please refer to p883, "Interest Rate Models - Theory and Practice", 2nd edition

<t>Looks like you are talking about calibration to the historical data. I guess there are two possibilities:1) the rate in the CIR is a non-centralised chi-square distribution, so if you are able to find the pdf of this one then you can use the (quasi) MLE to find the parameters;2) alternatively you...

Can anyone give a clue of how to solve:Minimise: x1^2 + x2^2 + ... xn^2s.t. f(x1,x2,...,xn) = C where C is a known constantIf I understand correctly this is equivalent to find the shortest distance from a hypersphere f() to the origin.

<t>Changing eigenvales is also feasible (maybe easier since the constrains are each bigger than 0 and sum equal to n).For a trivariate, suppose the upper triangle is 0.5,0.8, -0.1. The eigenvalues are 1.90, 1.09 and 0.01.Now slightly changing them to 1.95, 1.04 and 0.01, you get a new correlation ma...

Suppose the original correlation matrix is [1 0.5;0.5 1]. The eigenvalue/eigenvectors are hence [1.5 0.5] and [0.71 -0.71; 0.71 0.71].By slightly change the eigenvector while still keeping it orthogonal, for example [0.8 0.6; 0.6 -0.8] the new correlation matrix becomes [1 0.48; 0.48 1].

Isn't that just the differentiation of NPV of your annuity to the interest rate (or more precisely a parallel shift of the interest curve)?

"Analysis of Financial Time Series" by RS Tsay has the answers to both of your questions - by the way when I use EVT I usually use the non-parameteric method because the MLF sometimes are extremely non-linear (not surprisingly Excel solver can't handle it).

<t>Provided that I have one interest rate model well calibrated to the plain-vanilla swaption prices, and one equity model well calibrated to the plain-vanilla option prices, is it possible to use the market price of a simple hybrid swaption to calibrate the spot correlation parameter between the in...

You should read this paper:How Relevant is Volatility Forecasting for Financial Risk Management? Peter F. Christoffersen & Francis X. Diebold.