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Questions about models for the valuation of option contracts.

5 votes

Bachelier model call option pricing formula

You might want to differentiate between the growth rate $\mu$ and the discount rate $r$. @Gordon's solution is the most logical thing to do, given the question. However, in practice, it is not uncom …
  • 1,312
0 votes

use Monte Carlo or FDM to price Basket option

In finite difference methods, assuming the Basket is composed of $p$ assets, the solution of systems of size $N^p$ is going to be involved where $N$ is the grid discretization size per dimension. With …
  • 1,312
3 votes

Which stock tick has its geometric asian call?

They are not traded, even Over-The-Counter (OTC). Asian options with arithmetic averaging are traded. The geometric Asian may be used to derive a closed-form approximation for the arithmetic variety …
  • 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

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. Although the mid is a better idea in ge …
  • 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
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 …
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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 …
  • 1,312
0 votes

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

Using a cubic spline or worse, SVI is overkill to find the at-the-money (ATM) volatility when it is not quoted by the market: both approaches are global in the sense that a small change of one of the …
  • 1,312
1 vote

Smoothing of the payoff function as a terminal condition for numerical option pricing

Another approach would have been to use some projection as in Pooley and Vetzal Convergence remedies for non-smooth payoffs in option pricing. In your case, it may be a projection of the initial cond …
  • 1,312
1 vote

Mixing Black Scholes with SABR

In your first step, you will want to calibrate $\alpha, \rho, \nu$, and probably not $\beta$. See the related question Calibrate a SABR model? How close your option price is from the market price wil …
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