Statistics: Posted by fk — October 19th, 2018, 4:52 pm

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I am trying to value a cross currency amortising swap with knock out features.

How will the foll. conditions affect the valuation and the discounted cash flows :

1) A Conditional Payment is made if the knock out event has not occurred : Max(100-USDJPY,0%) / USDJPY * 50% * USD Notional.

Is this added to the total payout after the swap is valued ?

2) No Conditional payment is made if USDJPY is greater than 125 till maturity of swap.

3) A Contingent payment is made if USDJPY is less than 100.

Pls advise.

Thanks.

Statistics: Posted by nira — October 19th, 2018, 4:30 am

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Statistics: Posted by Amin — October 18th, 2018, 7:15 pm

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"Because levered equity is an option on the firm, variations in asset idiosyncratic risk (ivol) induces a negative relationship between equity ivol and expected returns. We show that the effect is caused by the nonlinear payoff of equity and the law of one price, and is present in all but risk-neutral economies. We test the cross-sectional predictions of our theory by contrasting the ivol-return relationship at the equity and asset levels. The ivol-return relationship is stronger for equity than for assets, and stronger for more levered firms---consistent with the theory. We test also the time-series implications of the theory. Time variation in asset ivol causes time variation in the option value of equity that translates into time varying risk factor loadings. Unconditional alpha subsequently becomes biased when asset ivol correlates with the market price of risk. We show empirically that a conditional CAPM that accounts for time variation in equity nonlinearity helps explain earlier findings that high-minus-low ivol-portfolios generate negative unconditional alpha."

"The implications of the analysis thus go beyond equity: One should expect to find correlation between ivol and expected returns for any derivative with non-trivial nonlinearities, be it real or financial. Ivol is thus truly a “characteristic” in asset pricing models that do not explicitly take nonlinearities into account, and is neither an “anomaly factor” nor a “priced risk factor.” Indeed, the absence of ivol-return correlation may indicate deviations from the law of one price."

Statistics: Posted by Collector — October 17th, 2018, 11:04 pm

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[$](\frac{\partial X_0}{\partial Z_0})^2 E(Z_0 )^2+ (\frac{\partial X_1}{\partial Z_1})^2 E(\rho Z_1)^2 + 2 \frac{\partial X_0}{\partial Z_0} \frac{\partial X_1}{\partial Z_1} E[Z_0 (\rho Z_1)][$]

[$]+ .25 (\frac{\partial^2 X_0}{ \partial {Z_0}^2})^2 E (Z_0)^4-.25 (\frac{\partial^2 X_0}{\partial {Z_0}^2})^2 ({E(Z_0)}^2)^2 [$]

[$] +.25 (\frac{\partial^2 X_1}{ \partial {Z_1}^2})^2 E (\rho Z_1)^4-.25 (\frac{\partial^2 X_1}{\partial {Z_1}^2})^2 ({E(\rho Z_1)}^2)^2 [$]

[$]+.5 \frac{\partial^2 X_0}{\partial {Z_0}^2} \frac{\partial^2 X_1}{\partial {Z_1}^2} E[{Z_0}^2 (\rho Z_1)^2] -.5 \frac{\partial^2 X_0}{\partial {Z_0}^2} \frac{\partial^2 X_1}{\partial {Z_1}^2} (E[ Z_0 (\rho Z_1)])^2[$]

=[$](\frac{\partial X_0}{\partial Z_0})^2 E(Z_0 )^2+ (\frac{\partial X_1}{\partial Z_1})^2 E( Z_1)^2 [$]

[$]+ .25 (\frac{\partial^2 X_0}{ \partial {Z_0}^2})^2 E (Z_0)^4-.25 (\frac{\partial^2 X_0}{\partial {Z_0}^2})^2 ({E(Z_0)}^2)^2 [$]

[$] +.25 (\frac{\partial^2 X_1}{ \partial {Z_1}^2})^2 E ( Z_1)^4-.25 (\frac{\partial^2 X_1}{\partial {Z_1}^2})^2 ({E( Z_1)}^2)^2 [$]

Statistics: Posted by Amin — October 17th, 2018, 12:33 pm

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Using the variance for standard normal and its powers, we can easily calculate the local variance of X at the nth subdivision.

The only problem is that Z is perfectly correlated across time in our Ito-Taylor density simulation method while it is totally uncorrelated across time in reality so we have to make an adjustment in the value of Z that we use for simulation of Ito-Taylor density simulation method.

if [$]X_0[$] denotes the existing density variable and [$]X_1[$] denotes the innovations density variable, the true variance that is the right variance at the certain subdivision after taking the innovation simulation step should be

[$](\frac{\partial X_0}{\partial Z})^2 + (\frac{\partial X_1}{\partial Z})^2+.5 (\frac{\partial^2 X_0}{\partial Z^2} )^2 +.5 ( \frac{\partial^2 X_1}{\partial Z^2})^2 [$]

while Ito-Taylor simulation assumes complete correlation for the Z's across time and their variance without any adjustment turns out to be far greater. This variance can also be very easily calculated.

Again we have to make sure that Ito-Taylor simulation method variance matches with the true variance of the SDE at that particular subdivision. This can also be easily done. This is not much more difficult than what we did for one derivative case and requires slightly altering the analysis on the same lines. And then we will advance the SDE density with different local scaling of hermite polynomials on each subdivision so that local variance simulated with Ito-Taylor density simulation method matches with the true simulation variance.

I hope to post a full-fledged program that calculates the true density with Ito-Taylor density simulation method in a few days.

I am travelling tomorrow so will post more details on Tuesday.

Statistics: Posted by Amin — October 14th, 2018, 5:30 pm

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3-month LIBOR is not a compounded interest rate, but is typically quoted as a money market rate with the actual/360 day count. So, the PV of $1 discounted at 3-month LIBOR would be 1/(1 + LIBOR*days/360). Days are the number of days in the 3-month period, In some currencies you might use 365 instead of 360.

Statistics: Posted by DavidJN — October 14th, 2018, 5:06 pm

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I have a simple question on Libor rates. When people say "3 month Libor rate" what exactly is the 3 month referring to? Is it the compounding frequency, or the length of the loan?

Thanks

Statistics: Posted by billyx524 — October 14th, 2018, 4:17 am

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Statistics: Posted by Amin — October 12th, 2018, 1:19 pm

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Statistics: Posted by gatarek — October 12th, 2018, 10:23 am

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My question is: what is the best, modern and adviceable pricing technique (model) to price Mbs?

Now I have an opinion (is it correct?) :

There are three main methods to price MBS: econometric, option-based, intensity-based for prepayment.

I think that econometric methods are old with its regression based methods of 1980-s that brings OAS, it doesn't use the difference between P and Q measures.

Option-based approach uses optimal decision principles for pricing which does not exist in reality. And intensity based approach for prepayment modeling is modern, using full power of modern stochastic financial mathematics and does not introduce OAS. So, the last method, developed last years, is more favorable.

Am I right?

Statistics: Posted by Rfz — October 11th, 2018, 8:09 pm

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SGD-BB

SVRG-BB

?

Statistics: Posted by Cuchulainn — October 9th, 2018, 2:32 pm

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Too many positive waves ROCK THE BOAT.

Enough of this Kindergarten. When will we be able to read your article?

Statistics: Posted by katastrofa — October 8th, 2018, 12:03 pm

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