# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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### Binomial Option Pricing [duplicate]

We are currently working on the "standard" binomial option pricing. If the market agrees that a specific stock will raise by, let's say, 90% next period. At first glance, this seems to have ...
1 vote
64 views

### When does a closed form analytic solution exist/not exist for the value of an option given by the BS eqn?

I am new to the quantitative finance side of things( came from mathematical physics). I'm currently investigating numerical techniques for solving BS, which made realise when are numerical techniques ...
122 views

### Continuation value in Longstaff-Schwartz: Why the expected value?

In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by: \begin{align} F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
1 vote
41 views

### STOXX50 and VSTOXX joint calibration

I am currently researching the joint calibration problem of SPX and VIX. The idea is that: VIX options are derivatives on the VIX, which itself is derived from SPX options and should thus be able to ...
96 views

### What is the risk neutral expectiation of an option price given a move in spot?

Lets say we have a volatility surface for the SPX at time t with spot S. We consequently know the price of some call option at maturity T with strike K. What is the risk neutral expectation of the ...
97 views

### Problem matching prices of Black-Scholes vs. GARCH(1,1) in Duan (1995)

In the paper of Duan (1995) the author compare European call option prices using Black-Scholes model vs. GARCH(1,1)-M model (GARCH-in-mean). To be brief, the author fits the following GARCH(1,1)-M ...
399 views

### How to price very short dated options?

I was wondering if there is any industry standard in pricing very short dated options, from say 6h options down to 5 minute options. My thinking is that as time to expiry gets shorter and shorter, the ...
1 vote
137 views

### GARCH process simulation in R

I'm trying to learn how to simulate the GARCH(1,1) for option pricing using Monte Carlo. I need to learn how to code the equations for the stock log returns and the variance process. I'm trying to ...
151 views

### Best tool to find an optimal option? [closed]

I like to sell uncovered put options, using my valuation of the company as the strike price. I'm looking for a tool that takes stock identifier and strike price as input and outputs the optimal ...
414 views

### Bartlett's delta gives wrong signs for calls and puts

There is a paper by Bruce Bartlett introducing a modified delta for SABR model which accounts for the correlation between forward and volatility processes. The main result of the paper is that if $dF$ ...
160 views

### Pricing Quantos with Local-Stochastic Volatility model

I would like to price equity quanto options with the Heston Local-Stochastic Volatility model (LSV) but I am having hard time understanding how to apply quanto adjustment in such complex setup. When ...
100 views

### Exact delta-hedging for endogenous payoffs

I would like to derive the exact delta-hedging strategy in the Black-Scholes market to replicate the following non-standard endogenous payoff. The particularity is that the payoff does not only depend ...
71 views

### Theta Greek Max Curvature [duplicate]

how to solve it for max Theta Curvature? i'm looking for the pure math glyph formula.. it may be related to actually 3rd deriva & curvature function..
398 views

### Gamma for a basket option in Python - Finite Differences vs. AAD Autograd library using Heaviside Approximation

I have been trying to use the Heaviside Approximation for a simple basket option so that I can solve for Gammas with AAD (Adjoint Automatic Differentiation). This routine smooths the payoff function ...
259 views

### What is the Fair Strike in a Var/Vol Swap and how does it relate to its price? [closed]

I am a student trying to price volatility and variance swaps. People who price those two products usually try to get the "fair strike", and don't seem to care about the price. However, I ...
80 views

### Solve for spot price given delta [closed]

I can use Black Scholes or Bjerksund Stensland to solve for delta given spot price, strike, expiration, vol, interest rate, etc. But is there a direct solution to solve for spot price given delta, ...
30 views

### Binomial model returning linear IV smile when estimating for IV

So I've been attempting to align the Binomial model with the American put option price so that I can calculate accurate Greeks taking into account the optimal exercise boundary of these options. The ...
49 views

### Monte Carlo Derivative Pricing

In order to try and price some derivatives with payoff $H(S_T).$ I am going to calibrate a few models (BS, Heston and CEV) to some real world data. Then I will calculate option prices as follows: ...
259 views

### Question on Merton's self financing derivation

I'm reading Merton's Optimum Consumption and Portfolio Rules in a Continuous-time Model, and don't understand the step where he goes from discrete to continuous time. Specifically, my confusion is ...
320 views

### Intuition behind calendar spread max loss

With a calendar spread (buying back, selling front), max loss is defined as some variant of "maximum potential loss is the cost of opening the trade (Premium Paid − Premium Received = Total Debit)...
1k views

### Theta changes over time

Theta is the change of an options value with respect to time. But theta itself changes over time. Today's option theta is not the same as tomorrow's option theta. What is the greek name for this value?...
77 views

### How to improve fit in American options vol surface?

I am trying to model the volatility surface of index etfs (spy, iwm and qqq). I am using the CRR model with discrete dividends and the spot model. I find that for some cases there is a noticeable ...
1 vote
104 views

### Why fitting $\mathbb{Q}$ vs $\mathbb{P}$ measure Heston model if both fit to market

If both models fit their closed form formulas to market prices, why should I prefer a more complex model? ($\mathbb{Q}$ version has one extra parameter $\lambda$) Do valuation with dynamics work ...
196 views

### Questions about the replicating portfolio in the binomial model

I'm starting to teach myself quantitative finance and I've got several questions (marked in bold) regarding the replicating portfolio of a security in the binomial model. I'm following, among others, ...
1 vote
394 views

I am reading the article, where different approximations for the pricing of basket options are presented. I have tried to reproduce the result obtained by the Gentle's method in Python. We define the ...
332 views

### Risk free rate for currency option

I’m trying to price a call option on EUR/GBP exchange rate and it expires in 1 year. Should I use GBP Libor as foreign risk free rate in order to apply BS formula? The pricing date is 02/21/2023 but ...
31 views

### How to price an american put option on a dividend-paying stock? [duplicate]

There is no Black Scholes formula for the value of an American put option on dividend paying stock eithe has been produced ? Should I use the binomial model ?
1 vote
42 views

### Implying a probability distribution from option prices [duplicate]

I was reading this article, when I came across this text: Without using a complex options pricing model, one can use intuition to translate option prices into implied probabilities. For instance, the ...
79 views

### For derivatives pricing, does FEM actually ever outperform FDM?

Simple question that I was wondering about over during the weekend. I have done a little FEM during the last years and my university time and did not spend a lot of time with FDM. For a new job I have ...
1 vote