If I have a 5Y gov bond with 4% coupon priced at YTM of 2%. Does that mean that all gov bonds with maturity of 5Y should also have YTM of 2%?If I have a 5Y gov bond with 2% coupon, must its price be 100?Do assume that the gov bonds are similar in all aspects except for coupon rate.

<t>Say we observe actual stock prices S0,S1,...Sn in the real world and let us assume that they actually follow a GBM with constant drift and constant volatility.Question is, does the mean of log returns of the time series give us1) muor 2) rfPhrased in a different way are we assuming real world sto...

<t>I was researching what you said and I got Q-dynamics for each different country index, below equation repeated many times for different Ss.To derive the correlation to use in simulating each of the dWt1, dWt2 can I use as proxy the actual realized correlation of log returns of the different index...

<t>derivation of quanto adjustment is shown in Paul Wilmott's book for yen dollar and Nikkei Dow index (2 assets)Can we generalize the result to more than 2 assets, ie 2 stocks, 1 in HKD and other in JPY while the payout is USD.Is there a book or paper that shows the derivation for this generalizati...

<t>his simple interest rate model in Q measure isr is r(t) for abbreviationdr = mu r dt + sigma r dWLet's assume that mu and sigma is constant through time.If I was given a historical time series of 1 day rates (approximately short rates), In a GBM, the log-returns are normally distributed so the ML...

A trader asked me why I cannot just use correlation measured from interest rates and the stock prices

<r>Assuming the 2 following equations are under Q measure and are used for Monte Carlo pricing, I'm trying to measure rho empirically from real time data series of Stock prices and interest rates.Stock GBM1. dS(t) = rS(t)dt + sigma S(t) dz1Vasicek2. dr(t) = a ( b - r(t) ) dt + sigma dz2dz1 and dz2 a...

Is the sigma the same for both objective/real work probability measure vs the risk neutral?

yes, let's assume that I do not need pricing accuracy but rather the simplest model but with the concepts right.

Can I do a simple approximation by taking mean and stdev of log returns of 1M rates to give me mu and sigma?

For stocks, drift is risk free rate, so my question is for RB, what is the appropriate drift rate to use?

<r>Based on wikipedia entry, <URL url="http://en.wikipedia.org/wiki/Hull%E2%80%93White_modelit">http://en.wikipedia.org/wiki/Hull%E2%80%93White_modelit</URL> says that r(t) is normal only when theta is constant.However, I see that on this forum, some have said it's normal.I'm interested in the parti...

<t>In the usual case of 2 GBM assets, correlation is taken for the log returns of each underlying.In this case where one of them is interest rate with the Hull White equation which is not GBM, do I still take the log return of the short rate to measure the realized correlation?I tried to derive the ...

<t>I was trying to use cholesky factorization when I realized that my choice of interest rate model (Hull White) is not GBM while my FX model is GBM. Is there still a way to use cholesky?If I were to model them separately as suggested above, wouldn't I be assuming that the 2 random variables are ind...