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by manolom
November 15th, 2011, 11:20 pm
Forum: Student Forum
Topic: existence of moments
Replies: 2
Views: 15641

existence of moments

<t>QuoteOriginally posted by: ColdKing If E[|X|^k] exists, then E[|X|^m], for all m<k exists.Have learnt the proof of this statement long before. Now forget how to prove it. Does anybody still remember or which book/web reference has this proof? Thanks!You need to check that, for any 1<=n<k, To do t...
by manolom
November 15th, 2011, 8:36 pm
Forum: Student Forum
Topic: swaptions
Replies: 17
Views: 17496

swaptions

<t>QuoteOriginally posted by: Bazman2 Therefore as in the original post if the 1y*1y is trading at 25% and the 1y*2y is trading at 20% you can work out what the 1 year 2 year forward vol should be?Vol(1y2yf)^2=((vol(1y1y)^2*1)-(vol(1y2y)^2*2))/(1)Actually it'd be Vol(1y2yf)^2=(-(vol(1y1y)^2*1)+(vol(...
by manolom
November 14th, 2011, 11:00 pm
Forum: Student Forum
Topic: are there bounds on vega?
Replies: 2
Views: 15804

are there bounds on vega?

Wrt BS vega, correct me if I´m wrong, I´d write:
by manolom
October 31st, 2011, 11:28 pm
Forum: Technical Forum
Topic: Bootstrapping OIS, Fed Funds Curve
Replies: 3
Views: 20268

Bootstrapping OIS, Fed Funds Curve

Assume the flat (i.e., no spread), floating leg is worth par.
by manolom
October 31st, 2011, 11:24 pm
Forum: Student Forum
Topic: Martingale equality
Replies: 5
Views: 16424

Martingale equality

You are missing an E:
by manolom
August 29th, 2011, 3:37 pm
Forum: Technical Forum
Topic: Modeling Spot Exchange Rate with Stochastic Interest Rates
Replies: 22
Views: 24111

Modeling Spot Exchange Rate with Stochastic Interest Rates

<t>QuoteOriginally posted by: list I think that for example equation d S(t) = (rd (t) - rf(t)) S(t) dt + sigma (rd (t) - rf(t)) S(t) dW(t)looks more analytically realistic thand S(t) = (rd (t) - rf(t)) S(t) dt + sigma S(t) dW(t) ( 1 )This means that the exchange rate between 2 currencies with simila...
by manolom
August 26th, 2011, 11:13 pm
Forum: Student Forum
Topic: caplet as bond put
Replies: 15
Views: 19920

caplet as bond put

You cannot use Black's formula to price an option on a zero coupon bond, as the underlying (the price of a zero coupon bond) is not lognormal (because the forward rate is).
by manolom
August 23rd, 2011, 10:34 pm
Forum: Numerical Methods Forum
Topic: Pricing this 7.5 year swap - True newbie :(
Replies: 4
Views: 20559

Pricing this 7.5 year swap - True newbie :(

<t>Do you mean the swap rate for an IRS starting today, maturity 10/11/20 ? If the curve is as of today, and the swap rates have the same conditions (day count convention, frequency of payments, ...) as the one you want to price, I'd interpolate the maturity date in the mkt swap curve, as it lies be...
by manolom
August 23rd, 2011, 9:18 pm
Forum: Student Forum
Topic: Quanto plain vanilla formula for FX rate
Replies: 7
Views: 19461

Quanto plain vanilla formula for FX rate

<t>I still have doubts about whether correlation should be 1 or -1.I obtain that the quanto adjustment to the drift of the exchange rate USDperEUR is -1 x sigma x sigma, where sigma means the annualised vol of returns of the exchange rate. A change of measure adds the term rho x sigma(underlying) x ...
by manolom
August 23rd, 2011, 8:24 pm
Forum: General Forum
Topic: ho lee monte carlo?
Replies: 4
Views: 20391

ho lee monte carlo?

<t>QuoteOriginally posted by: nealsmith but when I generate, say, 1000 paths, and then find the mean of a simple ATM caplet payoff L*dt*(r_{t_k}-K) I'm off by a factor of 100 from the BS price.Try generating more paths. Double check that there are no constants missing, that you discount the payoff, ...
by manolom
July 14th, 2011, 7:03 pm
Forum: General Forum
Topic: FRA
Replies: 7
Views: 19316

FRA

<t>Many (most?) books still neglect the multi-curve paradigme (one curve for disc., as many curves as different tenors for forwarding) and they simply use "LIBOR". Reality is more complex - there are many other inter-bank offer rates, presence/absence of collateral, ... The OIS curve is assumed to b...
by manolom
June 23rd, 2011, 9:30 pm
Forum: Student Forum
Topic: How to argue that a self financing hedging strategy is a martingale?
Replies: 4
Views: 18769

How to argue that a self financing hedging strategy is a martingale?

<t>QuoteOriginally posted by: cedicon the self-financing hedging strategy is a martingale? ...I'd say "the discounted value of a self-financing portfolio is a martingale under the risk-neutral probability." The change to the Risk-neutral measure makes the drift equal to r. Discounting (play around w...
by manolom
June 23rd, 2011, 9:13 pm
Forum: General Forum
Topic: wiener process/brownian motion
Replies: 24
Views: 69257

wiener process/brownian motion

It is right - except for a couple of missing E's. Fubini allows you to change the order of E (actually, an integral) and the explicit integral. Remember that the odd moments of a zero-mean normal distribution are equal to 0.
by manolom
March 23rd, 2011, 6:22 pm
Forum: Technical Forum
Topic: very high forwards in LMM
Replies: 12
Views: 21759

very high forwards in LMM

30,000? It looks like there may be something wrong - compute the mean and variance of the resulting forwards and check whether it makes sense or not.
by manolom
March 21st, 2011, 8:39 pm
Forum: Technical Forum
Topic: Appropriate measure?
Replies: 3
Views: 20772

Appropriate measure?

Numeraires are required to not make payments during their life.
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