Tag Info

New answers tagged

0

I think the yield curve is not what you need here. The idea is to have a model for the dynamics of the bond process $dB(t,T)$ (which you can compute by having dynamics for short-term interest rate $dr_t$. A common assumption is to use Black 76 model with $F = B(0,T)$ if I remember well. You will also need to know the volatility $\sigma$ of your bond prices. ...


1

The math is actually simpler than what you proposed. Z-Spread is always computed as the parallel shift in a zero curve required so as to reprice the cash flows to a bond's cash flows; i.e., you solve for the $s$ in $$ P + AI = \sum_{i=1}^N c_i \cdot d(t_i) \cdot e^{-t_i \times s} $$ In the multi-curve world, you simply compute both the LIBOR OAS and OIS OAS ...


2

It is a Wiener integral as your integrand is a deterministic function of time. It is known that the Wiener integral is stationary gaussian process with independent increments. So $z(t) \sim \mathcal N\left(0, \int_0^te^{-2k(t-s) }~ds\right)$ and $(z(t)-z(s)) \amalg z(u), \ \forall u,s,t \in \mathbb R_+ \text{ such that }u\leq s, s\leq t $ or alternatively ...


0

I always thought doing $y(t,T) = \frac{-ln(P(t,T))}{T-t}$ was a quick good approximation, it applies when the bond price is calculated in continuous time


1

Are you familiar with the concept of yield-to-maturity (YTM)? Here you find all necessary steps. You first calculate using the current price and the cashflows. Then as you can see in the paper provided a bond with coupon rate equal to its YTM is priced at par (100) and thus the price equals its face value.


0

negative convexity, most likely, will imply that bond has embedded option. i.e. bond holder sells call option to bond issuer. therefore you'll have negative gamma position = collect option premium and short volatility.


1

I am going to assume that the only thing you are interested in is convexity and the many other aspects as well as the suitability of focusing on a single measure are not addressed. In such a general setting more positive convexity provides, as you have already outlined, for the potential to increase prices at a faster rate as a response to interest rate ...


4

you can view a bond as a floating rate note plus a swap from floating to fixed. Floating rate notes are always at par after coupon payments (ignoring credit risk...) so the pricing of a bond is the same as that of a swap. So the pricing of a callable bond is the same as that of a cancellable swap. A cancellable swap can be viewed as a swap minus the ...


1

There was a pretty good article covering this in Wilmott Magazine a while back. It covered the somewhat more general case of Callable Constant Maturity Swap Steepeners. You can ignore all the machinery around the CMS coupons if you are just treating standard callable bonds. That is to say, in Equation 8, you just need to set the multiplier $m$ to zero. ...


0

That's queer that you found nothing. Perhaps this project will be helpful. Let me know if you have questions about it.



Top 50 recent answers are included