# get base asset price for bond future

Is it possible to obtain the base asset price (underlying price) for futures using the first and second periods future.

like let's say we have $FGBL_1$ first future and $FGBL_2$ second future.

$FGBL_1 = e^{(1+R)*T_1}*B$
$FGBL_2 = e^{(1+R)*T_2}*B$

so by dividing them I can get $\frac{FGBL_2 }{FGBL_1} = e^{(1+R)(T_2-T_1)}$ where $T_1-T2 = 3$ months so after this I can isolate $R$ and use it to get B-base asset?

Is it right for bonds futures generally and specifically FGBL (German Bund futures)?

• It seems like a very poor method. First of all the "base asset" (actually one of several bunds satisfying requirements which can be delivered) is priced not based on futures_price, but futures_price*conversion_factor (where the conversion factor is definitely NOT equal to 1). Second the bund may pay a coupon between now and delivery, which you have not taken into account. Third the interest rates to T1 and T2 may not be exactly the same (term structure effect). There are many complexities of bond futures which you are neglecting. – Alex C May 10 '18 at 16:16
• de facto there is one CTD bund, how can I modal the coupon which the bund pay? – MSm May 10 '18 at 16:16
• @Msm It might help for you to clarify on what you're trying to accomplish, because at first glance, I agree with AlexC that this is not a good idea. Also, it's feasible that two bunds are competing for CTD status, in which case the futures behaves as a probability-weighted average of two bunds, instead of tracking one CTD... – Helin May 13 '18 at 20:27

The price of a bond futures contract is dependent on a number of variables;

• The base price of the underlying CTD bond asset
• The conversion factor of the bond price, which is a technique to 'equate' bonds under the specific contract terms of the future.
• The repo rate to delivery of the bond future.
• The net basis, reflecting the deviation from arbitrage free pricing, due to effects such as optionality on the CTD bond from the delivery basket.

You then have that:

$$F = \frac{P(1 + d R)}{C} - N$$

d = day count fraction, F = Future price, C = Conversion factor, N = net basis, R = repo rate, P = Bond asset price.

Of these variables the conversion factor is fixed and should be considered known, but the repo rate is often highly uncertain and can be different prices for different entities depending upon their access to interbank market or through dealers, and the bid/offer margin can be high, so is a source of inaccuracy. The net basis is usually an observable unless you have some form of stochastic modeller and can have a view on its value.

Having two calendar spread prices is not necessarily of any benefit for two reasons: 1) the two repo rates can be fundamentally and significantly different because of the different settlement data, 2) the CTD bonds are not guaranteed to be the same and fairly often will be different.

A word of warning: if you intend to use, as a proxy, a conversion factor of 1 and derive a theoretic futures price based on the theoretic bond of the futures contract specification with some good estimates for repo rates and a net basis of zero and compare the prices you will not yield any valid metrics since the fundamental differences you detect will reflect the nuanced difference between potentially different CTD bonds and the different levels of optionality of the respective baskets. And if you misestimate the repos only slightly your analysis may give a reversed conclusion since this formula is highly sensitive.