Questions tagged [swaption]
The swaption tag has no usage guidance.
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Bucketed gamma for swaptions
For a long 7Y1Y payer swaption, I understand that the overall gamma will be positive.
I see gamma to be positive in 7Y tenor and negative in 8Y - why would that be the case?
Intuitively, how would ...
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Forward implied volatility
Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ?
If it is impossible, why do we hear sometimes "being long a long ...
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Mid-curve swaption
I would like to know how the mid-curve swaption could inform us about forward volatility.
In my understanding it is a swaption on a forward starting swap.
Let us say the midcurve swaption expires ...
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1y10y vs. 10y1y Swaption
Say you have two identical payer swaptions, exception for their terms and tenors. In other words, suppose you have two payer swaptions: $1y10y$ and $10y1y$.
All other things being equal, according ...
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Question on volatility equation for CMS pricing
In "Full implications of CMS convexity (Cedervall and Piterbarg, 2012)", a.k.a. "CMS: covering all bases (idem)", the authors develop a CMS model equipped with an annuity mapping function which ...
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Turning an amortising swaption into a normal swaption
Is there a way to enter a trading strategy in which the notional of the cashflows of an amortising swaption become all the same?
For example, imagine the notional for the first four cashflows of an ...
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Put-call parity for cash settled swaptions
The Euro swaption market is changing from cash to physical settlement quotation in July 2018 $-$ see e.g. "Euro swaptions market prepares for pricign revamp (Risk, 2018)". When describing ...
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Bermudan Swaptions [closed]
Can someone explain, in layman's terms, the mechanics behind Bermudan Swapttions ( without having recourse to pricing models )?
Why are they popular? when are they used ?
How are they hedged i.e ...
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The "I want to price swaptions" request
In a small buy-side structure I recently had the following request : "I want to trade swaptions, I need to price them".
After a quick discussion the need is to price vanilla options on fix vs float ...
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Black-76 Model for Swaption Price and Greeks
I'm in the early stages of developing a swaption pricing model.
Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
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What exactly is the nature of swaption vol data?
Newbie here. I'm curious about underlying nature of the swaptions data on Bloomberg.
Define an arbitrary tenor and expiry swaption time series as
$X$(vol type, currency, reference curve) = [ $x_{...
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Obtaining swaption prices from lognormal volatility quotes
I am working with the following dataset from quandl: https://www.quandl.com/databases/CSWO (I'm using the sample dataset only). My question is how to obtain the swaption prices from the quotes given. ...
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Can you determine USD swap rate movement probability from OTM swaption premiums?
E.g., the USD 1y x 4y swap rate is currently 2.84%.
ATM receiver swaption , European exercise is currently at ATM premium of 1.15% while swaption premium at strike 1.5% is 0.15% or about 90% lower ...
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Change of Numeraire to price European swaptions
In the pricing of a European swaption, it is common to use the annuity factor $A(t)$ as the Numeraire. I was trying to write down the pricing formula via the bank account as numeraire to see if they ...
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Cash-settled swaptions
I was wondering, what is the motivation behind the payoff of the cash swaptions being multiplied by the swap annuity?
$$c(S_{\theta, T})=\sum_{i=\theta+1}^{T}\tau_i\frac{1}{{(1+S_{\theta,T}(\theta))}^...
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market value of a forward premium swaption
For a cash-settled vanilla interest rate swaption traded with forward premium paid in full at expiry of the option, what should the "mark-to-market" be during the life of the option?
Should it be ...
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Accreting swaption
Is there any literature on the maths behind the computation of the price of an accreting swaption in the LMM model (no monte carlo, closed formula or close enough...)?
Thank you!!
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Receiver Swaption and Callable Bond - Literature Proof?
I'm looking for a formal proof that a receiver swaption is equivalent to a callable bond.
I have only found some CFA Internet pages so far where this statement is considered as proven, tough I haven'...
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How to prrice a European swaption with floor?
I'm wondering how we can price a european swaption with a floor on the floating leg.
Assuming that we use the HW 1 factor model, how we can simultaneously calibrate the swaption ( on swap rate ...
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Swaption Price with Negative Swap Rate
To price Swaptions, I use the Black '76 model. I'm trying to update the model to handle negative interest rates. One such approach to doing this is detailed here. In particular I'm interested in the "...
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Swaption Trading
In most Banks, the Traders are provided with ATM Implied vols across different Swaption Expiry's and different Underlying Swap Maturities.(The ATM Implied Vol Cube)
If the trader wants to trade an ...
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Where can I find open swaption implied volatility data?
Anyone have a good place to find interest rate swaption implied volatility data? Does Bloomberg's python API allow access?
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Swaptions to calculate swap exposure for CVA
I am looking at using the swaption method to calculate the EPE and ENE on a swap over its life, to use in CVA/DVA calculations.
I have a number of questions, how well does this method work in ...
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Swaption Corridor Payoff Diagram
What does the payoff diagram look like for a long payer swaption corridor?
For example, suppose that I am looking at a long-payer $1 \times 10$-year swaption with 10Y swaps as the underlying. If I ...
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Swaption pricing
I am trying to understand the pricing of various types of swaptions.
Suppose I have a swap that starts in 3 months time. How would I go about pricing a swaption on this swap in the following cases:
...
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Volatility Parametrization Libor Market Model - Underspecified Model?
Does the volatility parametrization that I have chosen give an underspecified model? Which volatility parametrization in the Libor Market Model would suit the best for the particular case described ...
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Interest rates - Swaptions implied volatility - Volatility anchoring with Black and with normal volatilities
In a LMM+ with displacement factor a volatility anchoring technique is used, i.e. a long term volatility assumptions is applied, derived from historic time series. Should I adjust this historic ...
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Estimate the risk of swaptions
I would like to model OTM Swaptions. I can use some implementation of the Bachelier model (not B76 due to negative rates) and implied volatilities from Bloomberg.
For 10Y X 10Y (10 years option ...
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Pricing back swaptions corresponding to underlying swaps of Bermudan Swaption in calibrated LMM
I do not know to which swaption volatility matrix I have to calibrate the LMM in order to price back correctly the swaptions corresponding to the underlying swaps of a Bermudan Swaption.
My problem: ...
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Pricing Cancelable swap
Consider a first hypothetical, a swap.
Party 1 is paying 6 month Libor, semi-annually.
Party 2. pays $1+3*(\frac{Index_\color{red}{T}}{Index_0}-1) $ only at maturity. Say the notional is 1. $Index_t$ ...
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SABR Calibration: Normal vs Log-Normal Market Data
This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions.
So let us define
$C_{BS}(F_0,K,T,\...
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Accuracy Rebonato Swaption Approximation Formula among Different Strikes
Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes?
My foundings:
Let $0 &...
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Why can a swap option be regarded as a type of Bond option?
Why can a swap option be regarded as a type of bond option?
My idea: Suppose the swap rate of the swaption is $s$. Now consider a bond option expiring at $T$ with strike, $(P_K)_t = \dfrac{1}{1+s(T-...
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Swaption Volatility Cube arbitrage
How can I exploit an arbitrage by violating the following no-arbitrage condition (taken from the paper "Arbitrage-Free Construction of the Swaption Cube" by Simon Johnson and Bereshad Nonas):
Swptn(K,...
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Normal Black-Scholes model for swaptions isn't working properly
I just wrote two functions in Matlab which calculates the swaption prices based on the Lognormal model and on the Normal model, although I have the idea that the Normal model is wrong because the ...
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Is there any template of hull white one-factor calibration model?
Recently I would like to look for excel template of hull white one-factor calibration model using swaption data for my urgent task? However, it seems that I cannot find suitable one in the web.
...
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Why is there an upper limit on the premium of an ATM (!) call swaption in the Black76 model?
Trying to imply Black76 (where the forward swap rate is log-normal) volatilities as Bloomberg does in their VCUB screen we see holes at two regions:
at short maturities due to negative rates which ...
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Libor Market Model Calibration
Currently I am doing a research on the plain vanilla multi-curve framework Libor Market Model meaning that no stochastic volatility is involved. I had the idea to calibrate to the swaption market. In ...
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Valuation of option on amortized IR swap
I'm currently valuing swaptions using an implied volatility surface and Black's formula. This formula is given by
$$A (S\Phi(d_+) - K \Phi(d_-))$$
where
$$ d_{\pm} = \frac{\log\left(S/K\right) \pm \...
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Swaption on a swap with 0 year tenor
Any ideas on valuation of IRS swaption on a swap with 0 year tenor?
As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...
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Greeks of a swaption using Brigo
I struggeling with calculating the delta of a swaption. In the interest rate case I usually mess around with the multiple cash flows over time so that the discounting is more complex than in the ...
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Determining swaption prices using the characteristic function
There exist multiple techniques to determine call option prices that make use of the characteristic function. These techniques boil down to some integral expression of the option price in terms of the ...
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swaption model for forward swap rate
I have another question about interest rates. In this case it is about swaption and how to come up with a pricing formula. For the rest of my question I use the notation from Brigo. The payoff of a ...
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How to calibrate the Hull-White model using cap prices?
I'm given cap prices and swap rates, and i'm trying to calibrate the Hull-White model to them. I then want to use the model in order to price a swaption.
I know that the model can be calibrated from ...
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Price 3m libor autocap with LMM calibrated on 1y swaption data
I need to calculate a price of an autocap contract which is
An autocap is similar to a cap, but at most γ ≤ β caplets can be
exercised, and they have to be automatically exercised when in the
...
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LMM. Calibration to swaptions by Brigo and Morini. Volatility of swaption that matures at T=0
I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini.
I ...
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Calibration Problem in the LMM-Skew (Shifted Diffusion) Model
I have implemented the LIBOR market model (LMM) and I am quite satisfied with the results. I have now added a skew to the model as described in 10.1 of Brigo/Mercurio. That is, I have replaced the SDE
...
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Machine learning for non optimal behaviour
I was working on the pricing of complex bermudean swaption when I noticed that the exercise is often (very) subobptimal. It seems that the clients are more sensitive to past growth or drop in rates ...
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American Swaption Heding with Malliavin Calculus
Hedging American Swaption
Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t.
$$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
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Swaptions vol trading lognormally
What does this mean:
"Front-end vols have been trading lognormally while longer tails have traded normally."
I read this in a research report, in the context of ...
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