Thank you all for your replies, I'll try to cover some questions:
That's precisely the problem
Or are the govie futures not on the same underlying govie as your option?
. Govie futures underlying is the so called "cheapest to deliver" (CTD) bond. I'd say that, if the underlying of my otc bond option is the CTD
(or extremely similar in terms of duration) then I'm pretty much fine.
The difference is just going to be represented by the "conversion factor" of the future and the CTD. In general the premise is not true
: customers would like to underwrite options on whatever bonds they like. Such bonds may differ wildly (in terms of duration) from the CTD.
without trade how would you ascertain the correlation?
I completely agree. Thing is, all the bonds are "correlated" in the sense that they share the same yield curve (let's leave aside problems like on-the-run or off-the-run bonds). And the sensitivity of the bond price to the yield curve is the duration (and the convexity for 2nd order). Let's just say "I cannot trade in the bond, but everyone else can. I can trade only in futures and options on futures".
So I was wondering how to replicate an option on a bond BUT
delta-hedging it with futures (underlied by a probably different bond) and (possibly) vega-hedging it with options on futures. Of course we are talking about futures on bonds on the same yield curve (but as I said, different duration and yield than the underlying of my option).
EXTRA -> Let me add some real-life examples: Italy Govies market.
Only one future is really liquid (CTD is some 10yr benchmark bond Italian govy). This future is liquid only at 2 IMM dates (say March and June). Options on this future are liquid only at the same dates (say March/March and June/June). Now, if you ask me to write a bond option on the CTD, I got everything I need. Maybe I'll have to interpolate here and there for the exact maturity and strike, but still. What if you ask me to write an option on the 5yr benchmark? No futures on that bond (therefore no options). But I would like to come up with a price based on a replication strategy (as I said, straight Black-like assumptions) involving only those liquid futures.