Using the US as an example, the Fed closely controls the Federal funds rate, which is an overnight rate (not the yield on Government bonds). Usually therefore, the yield on government bonds is ...

Yes, the IRR is the same regardless of the prepayment date. The only thing that varies is the life of the loan.

How about trying a simple rule for early exercise. For example , exercise if stock > X, where C could be a constant or a vector. Chose X to maximize the option value.

Most banks consider this convexity too small to worry about. A typical approach is to model a mtm basis swap using notionals that correspond to the fx forward rates for each period. Every day these ...

My intuition is that your expected p/l from delta hedging is the same, regardless of what vol you use at each step (since this just changes your series of spot transactions, each of which has zero ...

The discount rate for 2) should be a risky rate $r + \lambda$, although we must talk about how to determine $\lambda$. If you have sold an uncollateralized put option, the put option is an unsecured ...

The Var depends only on the daily changes in futures price. So you create a series of daily changes and you simply omit the day when the roll occurs.

Here's a simple hypothetical example: Portfolio A = a single stock priced at 100 which can either go to 99 or 101 each with probability 0.5 in one year. The annual standard deviation is 1. The ...

The explanation that works for me is that what constitutes risk for a US investor (i.e. Making or losing money measured in dollars) is different from what constitutes risk for an Indian investor ( i.e....

What looks odd to me is that r(t) is used in two places. First, as the mortgage reference rate , and second as the short rate ( for discounting). I would have expected these rates to differ. In the ...

Loosely speaking, we use forward yields, not spot yields, to identify the market's estimate of yields in the future. Right now, the forward yields are higher than the spot yields, because the yield ...

Let lnA be N(0,1) and lnB be N(0,k) where we will let k tend to zero. Then B has all of its density at 1, so A+B>1 in the limit. Hence A+B is not lognormal.

The new curve will look a bit strange no matter how you do it, although 1bp is not such a big move that will render it "useless". Two ways of doing it, as you point out, are (a) use a spline method, ...

In your example, the buyer of the PRDC security is a Yen-based investor who gets long the BRL on a forward basis, on each coupon date and on the final maturity date. Because BRL is a lot cheaper ...

A few observations: the coupon yield curve is never going to be smooth, because a high coupon Treasury and a low coupon Treasury with the same maturity do not yield the same. That's because in an ...

The price of a [K,K+dK] call spread informs you about the risk neutral probability of the underlying being above K. (Not in the interval (K,K+dK)). This is true regardless of any assumed distribution ...

For stocks, here are some possibilities: (i) you could assume the level of the VIX index as a measure of the sytemic volatility (ii) you could take the VIX, scaled by the beta of your specific stock,...

The change in value of an inflation linked bond is Change in Real Yield * Duration = (Change in nominal yield of non-linked bonds - Change in inflation expectations) * Duration Duration is ...

I think you are referring to the BTP Italia series of bonds issued by the Italian Treasury, aimed at retail investors and linked to the Italian inflation rate. These bonds are issued in Euro, have a ...

You can't. In a 1 factor model, if you calibrate the libor floor to market, then the swaption prices in the model are likely to be too high versus the market. That's because the difference between ...

Commonly used procedures are to hedge; when a 1 SD move has happened, or when your delta position exceeds some risk limit, or once a day, or based on your desired delta position. All are used. I ...

It doesn't have to imply negative forward vol. for example , 1month 20 Vol and 2 month 19 vol implies (approximately ) that 1 month vol in 1 month time will be 18.

The risk of a 6s vs3s basis swap is usually expressed in two dimensions a) the risk to the 6s 3s basis swap widening ( i.e. Increasing the forwards for 6s by 1bp in parallel while keeping the forwards ...

An example will illustrate things. Let's say usdjpy forward is 100 and you are considering a usd1mm worth of a 120 call on usdjpy, which entitles you to buy 1mm usd using 120mm yen. Let's say the ...

The last step (taking everything outside the expectation ) is invalid. The expression $E[\frac{S_{T'}}{P^{T'}_T}]$ is the expectation of the product of 2 random variables. As such, you need a model ...

Off the top of my head, if interest rates are zero or negative, then yes. Just borrow the purchase price and buy any asset. Sell later and pay off the loan. Otherwise no.

The 3s 1s basis cannot be calculated in an arbitrage sense. You can make some reasonable assumptions. For example , if fra/iOS is tighter on s forward basis than spot, then 3s 1s is likely to have a ...

First calculate Rent1 and Rent2 for the two futures. Then the expected daily move of the spread between the futures is Sqrt( Rent1^2 + Rent2^2 -2Rent1Rent2Rho) Where Rho= the correlation between ...