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 ...
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  • 487
6 votes
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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 ...
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6 votes
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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 ...
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4 votes
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Introduction to Multiple Curve construction

I've always enjoyed OpenGamma's white paper: MULTIPLE CURVE CONSTRUCTION. It's a solid starting point from an implementation perspective. Andersen & Piterbarg's "Interest Rate Modeling" (Volume 1)...
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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 ...
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  • 3,589
3 votes
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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 ...
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  • 753
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 ...
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3 votes

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

you have a missing element in your data - you need to take into account xccy basis. when you do so, then you would get the same valuation in both methods. the key is to remember that since your ...
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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 ...
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2 votes
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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{...
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  • 20.4k
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 ...
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  • 2,362
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 ...
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2 votes

Comparison of multicurve calibration methods

Predictability - we all know what a bootstrapped curve will do when we shift a value. A minimisation, however, could jump to a new minimum at any moment. They also have unpredictable performance; ...
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  • 3,589
2 votes
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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+(...
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  • 1,419
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). ...
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  • 5,030
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 ...
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  • 4,961
1 vote
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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 ...
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  • 3,589
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. ...
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  • 7,997
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 ...
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  • 7,997
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 ...
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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 ...
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  • 254
1 vote
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What is the difference between a benchmark yield curve, funding curve and a basis spread curve?

Benchmark yield curves: Make it easier for market participants to efficiently price interest rate products off such benchmark yield curves because there is a consensus and agreement on what serves as ...
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  • 14.1k
1 vote

Building curves using onshore or offshore JPY overnight rates?

Generally it is best to use the rates that best capture how the collateral of the instruments are priced. If the overnight collateral on the instruments is managed using offshore JPY depo, then this ...
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1 vote
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ZSpread in multiple curve framework

The math is actually simpler than what you proposed. Z-Spread is always computed as the parallel shift in a zero curve required so as to reprice the cash flows to a bond's cash flows; i.e., you solve ...
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