Questions tagged [calibration]

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6
votes
1answer
10k views

Breeden-Litzenberger formula for risk-neutral densities

Based on this topic: How to derive the implied probability distribution from B-S volatilities? I am trying to implement the Breeden-Litzenberger formula to compute the market implied risk-neutral ...
12
votes
2answers
8k views

How to calibrate a volatility surface using SVI

I've read the following paper by Gatheral and Jacquier and have several question regarding the calibration of a volatility surface in a arbitrage free way and some theoretical aspects. Let me first ...
4
votes
1answer
296 views

Estimating $\mu$ - only increasing $T$ improves estimate?

Assuming an asset price $S$ follows a geometric Brownian motion (GBM), the log returns $R$ are distributed as $$ R_i := \log\left(\frac{S_i}{S_{i-1}}\right) \sim \mathcal{N}\left(\left(\mu - \frac{\...
5
votes
2answers
3k views

pricing using dupire local volatility model

I am reading about Dupire local volatility model and have a rough idea of the derivation. But I can't reconcile the local volatility surface to pricing using geometric brownian motion process. If I'm ...
4
votes
1answer
3k views

How to get set the theta function in the Hull-White model to replicate the current yield curve

I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in $$ \mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t) $$ to ...
10
votes
3answers
6k views

Option Pricing Model Calibration In Practice

I'm curious how an option pricing model like the Heston model is calibrated in practice. Here's how I imagine it happens: Let's say I have access to the most recent option prices on a given stock ...
6
votes
2answers
4k views

Local volatility SVI parametrization

In this paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ for each slice $k \mapsto w(k,T)$: $$ w(k) = a + b\{\rho (k-m) + \sqrt{(k-m)^...
9
votes
1answer
369 views

Is a common approach to calibration reasonable?

"Model Calibration" article in Encyclopedia of Quantitative Finance states that . . . a common approach for selecting a pricing measure $\mathbb{Q}$ is to choose, given a set of liquidly ...
15
votes
2answers
16k views

How to calibrate Hull-White from zero curve?

I am interested in calibrating a Hull-White model to the market. I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ...
4
votes
1answer
618 views

LSV model calibration with only few quotes per maturity

At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic ...
3
votes
3answers
3k views

Implied Vol vs. Calibrated Vol

Consider the Black-Scholes model, in which the log stock return over a time period $\Delta t$ is given by $$ \log(S_{i+1}/S_i) = (\mu - \sigma^2/2)\Delta t + \sigma \sqrt{\Delta t} Z_i, \qquad Z_i \...
4
votes
2answers
474 views

Forward skew generated by Local Vol model

I'm digging into the properties of the Local Vol model and I become confused with statements made by authors in papers/textbooks (without explanations) like, "The forward skew in local vol model ...
6
votes
1answer
187 views

How to choose the martingale measure in incomplete markets

Hey I know that when market is incomplete, then we have to choose an equivalent martingale measure (I heard about Escher Transform martingale measure, Mean correcting martingale measure, minimal ...
3
votes
1answer
2k views

Instruments for calibrating Hull White Model

I have a few questions regarding hull white calibration, specificly for the trinomial tree model. 1.I am wondering what are the ideal instruments could be used for hull white model calibration? Cap, ...
2
votes
2answers
5k views

Historical calibration of Hull-White model

I have a question concerning 1-factor Hull-White model. For my master project I need to calibrate it to compute Counterparty credit risk metrics. I know that the model might be calibrated either for ...
8
votes
1answer
2k views

How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries. I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
2
votes
1answer
1k views

Hull White Tree Calibration 2

This is actually to extend the question I asked previously and to follow up Bernd's answers. This is the original link: Instruments for calibrating Hull White Model 1. As Bernd mentioned, it's ...
1
vote
1answer
1k views

Why co-terminal swaptions are that important?

Usually Hull & White is calibrated to co-terminal swaptions. When asking why specifically co-terminal, I get the response that it is just a choice and it depends on the use we intend to do with ...
0
votes
0answers
67 views

Two questions about COS method

Hey I have some problem with COS method. Here is the paper of Fang and Oosterlee https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.466.267&rep=rep1&type=pdf Why in table 1.1 they ...