correct what you say about shortening time to maturityit may not be relevant if you have week's horizon, but if you manage a large position which you intend to hold for a year or longer, you may want to know how much it is approximately. convexity is like an option and as such it has time value.

Related one:I have a question about the real theta of the exotic interest rate book. Previously, I broke down the time value into carry, financing, and theta. As you guess, the carry is accruals and financing is the internal capital charge. When I derive the theta, I use the same curve with 1 day shift, so the rate curve remain as it was yesterday. i.e. for zero rate, r'(t+dt;t+dt,T+dt)=r(t;t,T) In the case of the normal upward curve, this shift makes a roll profit. However, I have a doubt that it's not exact one. I think one should use 1 day forward curve, i.e. r'(t+dt;t+dt,T)=f(t;t+dt,T), because the current curve repersents the tomorrow's expected curve.For the volatility curve, sometimes called 'volatility theta', it can be derived by the same way. i.e. V'(t+dt;t+dt,T)=V(t;t+dt,T).Is it a right way to derive a real theta? give your comments, plz.

how do you calculate the accruals for a swap?and what is the internal capital charge wonjun?

I mean the accrued interests after 1 day, and the internal capital charge is the rate paid for financing. I divide these carrying PL from the theta. Anyway, back to the theta, Samsaveel, do you think just rolling down the curve is the proper way to calculate the theta? or today's implied forward curve? i.e. r'(t+dt;t+dt,T)=f(t;t+dt,T)

It doesn't matter what it is, as long as you're being consistent and don't double-count. I have seen this sort of pnl attribution done every which way.

wonjoun,,Martin has more depth in those matters.but I will give my input based on the system I am currently working with.the system holds everything constant and it rolls down the curve one day and calculates the dirty theta.then as you said the dirty theta is broken down to finance ,accrulas,and carry.but is the carry the finance less the accruals?can you shed more light on the concept of volatility theta and where it fits in the dirty theta breakdown?cheers.

Hi, Samsaveel.I intend to separate the time value of exotic book into carry/roll and theta. The former is what you mentioned in the earlier discussion, earned by holding the position 1 day, and the latter stems from option-features, proportional to gamma PL. Bond managers, in general, do not use the term, 'theta', talking about their PL. Assume IR swaps, we don't have the 'theta' but carry and roll.As Martinghoul said, how to divide the PL does not matter, if I do consistently, because today's loss or gain difference comes back in the future. However, there would be a bleed if I cut and put together improperly. When I use spot bpv, I'd better calcute the carry/roll by rolling down curve 1 day, i.e. r'(t+dt;t+dt,T)=r(t;t,T). Using the forward bpv, the rolling effect comes out by a delta PL as the forwards tilt.Martinghoul, do you think this is correct?For the vol theta, apply the same idea. Have you seen a question, "Can you make the position, short gamma and short theta (with a vanilla)?" After the consideration of funding, the case is impossible in a flat vol. You can get it from rolling the vol term structure.

QuoteOriginally posted by: wonjunHi, Samsaveel.As Martinghoul said, how to divide the PL does not matter, if I do consistently, because today's loss or gain difference comes back in the future. However, there would be a bleed if I cut and put together improperly. When I use spot bpv, I'd better calcute the carry/roll by rolling down curve 1 day, i.e. r'(t+dt;t+dt,T)=r(t;t,T). Using the forward bpv, the rolling effect comes out by a delta PL as the forwards tilt.Martinghoul, do you think this is correct?Sounds about right, wonjun, although I am not sure I understand your terminology correctly...

QuoteOriginally posted by: MartinghoulQuoteOriginally posted by: wonjunHi, Samsaveel.As Martinghoul said, how to divide the PL does not matter, if I do consistently, because today's loss or gain difference comes back in the future. However, there would be a bleed if I cut and put together improperly. When I use spot bpv, I'd better calcute the carry/roll by rolling down curve 1 day, i.e. r'(t+dt;t+dt,T)=r(t;t,T). Using the forward bpv, the rolling effect comes out by a delta PL as the forwards tilt.Martinghoul, do you think this is correct?Sounds about right, wonjun, although I am not sure I understand your terminology correctly...wonjoun,can you give more information as to what you mean by forwards tilt

Assume a normal upward curve and rate curve does not change several days. The MTM PL will be positive, stemming from carry and rolling, as you know.Next..Your risk manager measure a market risk with forward bpvs.The forward curve would tilt and makes a delta PL, even though the spot rate curve un-changes.Then, where is the money from?

do you mean spot curve,as in the short end of the curve remains the same?Thanks Wonjun