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A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

0 votes

use Monte Carlo or FDM to price Basket option

The framework for the computational effort order has been described in Broadie & Glassermann A stochastic mesh method for pricing high-dimensional American options and more explicitely with regards to …
  • 1,312
1 vote

Why is accuracy important in pricing American Options?

For OTC options, the pricing model may help you infer the price of the American option from European options prices. … The model also gives you a simple way to delta hedge and vega hedge your American options. …
  • 1,312
1 vote

Arbitrage-free IV surface definition vs. real arbitrage process

In general, you don't want to build one arbitrage-free bid surface and one arbitrage-free ask surface, since such surfaces would have no practical use. As you mention, any hedging will involve both bi …
  • 1,312
1 vote
Accepted

Interpolating implied volatility term structure when IV is sampled at fixed delta points

The iso-moneyness approach guarantees no arbitrage in terms of calendar spreads, but it is not proven it does not introduce some butterfly spreads at some interpolated time. See Arbitrages in the Vola …
  • 1,312
6 votes

Pricing of a Foreign Exchange Vanilla Option

The answer given is mostly wrong: @msitt uses a convoluted way without explicitly mentioning it (put-call symmetry) to actually give the price of a USD Put, not of a USD Call as requested. Here is a m …
  • 1,312
1 vote
Accepted

Option Prices And Calibrating The Heston Model Code Question

In your code sample, the market prices are given, in terms of vols (in the data array)...
  • 1,312
1 vote
Accepted

How to reduce variance in Monte Carlo using Control Variates when spot prices are decreasing?

Some of the assumptions here are wrong. The issue here is that $$S_0 \neq e^{-rT} E[S],$$ but $$F = E[S].$$ And thus Z should be Z=V-theta*(VC-exp(-rT)*F). If you output mean(VC) it's very clear. It s …
  • 1,312
2 votes

What causes the call and put volatility surface to differ?

The market will quote Call and Put options prices within a bid-ask spread. In order to imply the volatility, one may choose to use the bid, the ask, or the mid. …
  • 1,312
4 votes

Which volatilities should I use for Quanto Options?

The main issue with the answer from @quantuple is that the price does not converge to the Black-Scholes price when rho=0 or when the quanto adjustment is negligible. The question is answered in secti …
  • 1,312
1 vote

Pricing in the Heston Model

This is not the typical Heston stochastic differential equation (SDE). In the original Heston paper, the SDE is defined without $\lambda$, that is $\lambda=1$ and $v(0)=v_0$ not necessarily 1. In you …
  • 1,312
1 vote

Does high levels of vol-of-vol parameter in SABR lead to Arbitrage? (Something seems wrong w...

I can confirm there is no error in @Sanjay graph. I obtain the same plot with Obloj correction for the SABR formula. In fact, the popular SABR approximation formulas (Hagan or the further corrections …
  • 1,312
2 votes

Heston Model Integration Oscillations

This is a well known issue. There are three possible tricks: I am surprised that none of the answers so far mention the work of Lord and Kahl Optimal Fourier Inversion in Semi-Analytical Option Pric …
  • 1,312
4 votes

Is there a Dupire's Formula for put options?

It depends what you exactly call Dupire's formula. If you take the original formula, valid under zero interest rates and dividends (or equivalently, considering undiscounted option prices on the forwa …
  • 1,312
2 votes

What is the best book to learn about local vs. stochastic volatility, modelling and pricing ...

Such a question really invites me to recommend my own book Applied Quantitative Finance for Equity Derivatives, which you can buy on Amazon. The book devotes 200 pages to the subject of volatility. I …
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0 votes

Estimating at-the-money volatility where at-the-money option is absent from the market

The $z_i$ is the moneyness or log-moneyness for the three options around ATM considered. The paper also details least-squares approaches if you want to include more points around ATM. …
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