1
$\begingroup$

It is known that the price of an European call of maturity $T^*$ on zero-coupon of maturity $T$ is given by

$$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$

where $B(0,T)$ is the zero-coupon value at time $0 $ of maturity $T$ and $\mathbb Q_{T^*}$ is forward risk neutral measure. It's also known that $B(t_1,T_2)= e^{-(t_2-t_1)R_{t_2}(t_1)}$ what let me to the question:

How to calculate this price having the yield curve as the only input data ?

$\endgroup$
1
  • $\begingroup$ What is $R_{t_2}(t_1)$? I guess there is a typo. $\endgroup$
    – Richi Wa
    Jan 19, 2015 at 18:21

2 Answers 2

1
$\begingroup$

The yield curve gives you the tools to calculate everyhing that is derived from it. Derivatives from the yield curve only are e.g. - Fixed rate bonds - Forward Rate agreements - Floaters - Swaps.

All these are discounted cashflows or portfolios based on discounted cashflows and forward rates (which you can calculated from the yield curve).

If you calculate options (swaptions, options on fixed-rate bonds) then you will need the volatiltiy from the market. You need additional data.

It is just as with a stock-index option. I need the stock price, risk-free rate, dividend-yield estimate and (!) the implied vol. Any other vol different than the implied vol with give me a different price (different than the traded market price).

$\endgroup$
0
$\begingroup$

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.

Filipovic's book is an excellent reference for this (and much more).

$\endgroup$
2
  • $\begingroup$ @That Thanks for your comment. I know that. My question is all about how to calculate it just raving the Yield Curve as input and nothing else. $\endgroup$
    – Paul
    Nov 20, 2014 at 1:39
  • $\begingroup$ @Paul arf. I understand now. I know it's somehow in there but maybe specifying this (i.e. that you know Black is a solution but you don't want it) in the question would have made it clearer. $\endgroup$
    – SRKX
    Nov 20, 2014 at 1:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.