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11 votes
Accepted

Volatility adjustment for SOFR/OIS caplet referencing LIBOR vol

I will refer to Risk-Free Rates (RFR) for greater generality, instead of OIS or SOFR. There are two dimensions to your question, I will treat them separately. How to adjust a LIBOR vol surface to ...
Daneel Olivaw's user avatar
7 votes

Why is CSA currency OIS rate used in discounting instead of local currency OIS?

The problem here is that your market is not arbitrage-free: JPY OIS = 10% per day, flat USD OIS = 0% per day, flat USDJPY spot = 100 USDJPY Forward for tomorrow = 100 A quick sense check ...
Marcino's user avatar
  • 507
6 votes
Accepted

What is Dual Curve Bootstrapping? And how to do it, with an example?

A multi-curve means that you observe the discounting instruments (such as fed funds) and projection (libor, swap curve) and solve for all of them simultaneously; as opposed to bootstrapping separately ...
Dimitri Vulis's user avatar
4 votes

pricing in the case where payment currency and collateral currency are different?

TO answer the question in the comment. Suppose you have a USD cash flow receivable in 5yrs and you are trying to calculate the PV. You need to know the interest rate that you are paying on the EUR ...
dm63's user avatar
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3 votes
Accepted

Curve building dates overlapping impact on discount factor

There is no overlapping, the first instrument is tied to the LIBOR rate starting at $25/10/2019$, the second one is tied to the LIBOR Rate at $27/04/2020$. For the sake of clarity, let assume that ...
Canardini's user avatar
  • 553
3 votes

Why is CSA currency OIS rate used in discounting instead of local currency OIS?

To expand on Marcino's correct appraisal of the matter: arbitrage was introduced with the 4 pieces of market data. i.e. JPY OIS = 10% per day, flat USD OIS = 0% per day, flat USDJPY spot = 100 ...
Mr Batweed's user avatar
3 votes
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Lattice pricing of derivatives under multi curve framework (OIS and LIBOR)

There are many resources describing how to build a trinomial tree for the Hull & White model (for instance http://www-2.rotman.utoronto.ca/~hull/downloadablepublications/TreeBuilding.pdf), and ...
Antoine Conze's user avatar
3 votes
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Recommended Instruments (and sources) for Constructing Money Market Yield Curves

A plethora of instruments, a menagerie of curves Different instruments are traded in different ways, and relate to a collection of curves. Floating rate instruments depend on some index in order to ...
Phil H's user avatar
  • 3,669
2 votes
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Building a consistant Forward curve in the multicurve framework

One possible solution is to build "synthetic" short term 6M IBOR deposits by extrapolating for $T < 6\text{M}$ from the 6M IBOR deposit and 1x7, 2x8, etc. 6M IBOR FRAs as I have seen done in ...
Antoine Conze's user avatar
2 votes

expected change in value of a derivative in a multicurve framework

self financed portfolio will give you : $$ dV_t = r_F(t) \underbrace{(V(t)-C(t) - \Delta S_t )}_{\text{cash position}} dt + r_C(t) \underbrace{C(t)}_{\text{posted collateral}} dt + \underbrace{\Delta ...
M. Jeunesse's user avatar
  • 2,422
2 votes
Accepted

Yield curve bootstrapping: direct market rates vs discount factors interpolation

If we interpolate between the two libors $L_1$ and $L_2$ (spot rates) with maturities $T_1$ and $T_2$ the discount factor at $T\in(T_1,T_2)$ is $$ P(T)=\frac{1}{1+TL(T)}=\frac{1}{1+T\frac{(T_2-T)L_1+(...
Kurt G.'s user avatar
  • 2,023
2 votes

Curve building dates overlapping impact on discount factor

Your rates do not overlap. You have a 6M (185/360) rate of 5%. And a forward rate agreement where the 5.2% rate starts at the end of your initial contract (4/27/20) for a period of 6M (183/360). ...
AlRacoon's user avatar
  • 6,532
1 vote

pricing in the case where payment currency and collateral currency are different?

If I recall Cooking with collateral by Piterbarg (https://www.risk.net/derivatives/2194249/cooking-collateral) has the details but you effectively need to use FX swaps to get the basis adjust discount ...
river_rat's user avatar
  • 980
1 vote

Cash flow mapping on multi curve framework

From recollection don't you only map the fixed cashflows? If the 6m rate is 1% and your swap is at 0.5% then on a notional of 100 you map: 6m curve @6m: +1 OIS curve @6m: -0.5 If the 6m6m forward ...
Attack68's user avatar
  • 10.3k
1 vote

How to construct a GBP FVA curve from a USD FVA curve

There are two aspects to consider here. Aspect 1 is funding the notional of the Xccy swap and the coupons (strictly speaking this is not FVA). Aspect 2 is funding the MtM of the swap throughout the ...
Jan Stuller's user avatar
  • 6,098
1 vote
Accepted

Proper Method for pricing Interest rate swaps using dual curves

The price of something under OIS discounting is (supposed to be) the expectation of its value under a particular measure, which specifies the measure and the interest rate of the collateral account ...
Phil H's user avatar
  • 3,669
1 vote

Discounting in multicurve environment

OIS rates, and the OIS fixing, reflect unsecured lending on an overnight basis. OIS rates compounded for 1Y reflect unsecured lending for a 1Y period via rolling overnight loans for a 1 year period. ...
Attack68's user avatar
  • 10.3k
1 vote

Convexity in interest rate curve bootstrapping

Generally speaking there are more inputs that are required to precisely specify the multicurve structure, and they are potentially more important. For example consider constructing a EUR interest ...
Attack68's user avatar
  • 10.3k
1 vote

Libor Market Model Implementation

For example a Caplet with Expiry of 3year with tenor = 0.5 has to be priced (following the analytical formula) with the LIBOR rate L(0,2.5,3). Am I getting it right ? Thats right. The caplet hast a ...
TomDecimus's user avatar
1 vote

Which discount curve to use when valuing multi currency swaps

This is a "cheapest-to-deliver" option - in the absence of any restrictions, the rational investor would post whichever collateral class offers the best rate of return at each moment in time (of ...
atkins's user avatar
  • 264
1 vote
Accepted

expected change in value of a derivative in a multicurve framework

From $(2)$ of Piterbarg, \begin{align*} V(t) = \Delta (t) S(t) + \gamma(t), \end{align*} where $\Delta (t)= \frac{\partial V(t)}{\partial S}$, and $\gamma(t)$ is the cash account that satisfies \begin{...
Gordon's user avatar
  • 21.1k

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