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Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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Hedging with machine learning

I’ve been thinking about an interesting problem lately: Suppose I have a position in an exotic derivative. How can I automate the hedging process? Traditionally, one build a pricing model and ...
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1answer
89 views

Why my implementation of CRR model does not converge?

Recall that CRR (Cox-Ross-Rubinstein) model for option pricing is the usual binomial tree model with $u$ (up-factor) and $p$ (one of the risk-neutral probabilities) defined as follows: $$u = e^{\sigma\...
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28 views

Cash-or-nothing and Asset-or-nothing price derivation

I was wondering how to derive the price of a cash-or-nothing and asset-or-nothing option by trying to work out the expectation under the risk-neutral measure, while assuming that the underlying ...
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1answer
31 views

Value simple chooser option as a sum of call and put options

There is a well known formula for valuating the chooser's option price: $H_{chooser}=max\{C(S_t, K, T-t), P(S_t, K, T-t)\}=max\{C(S_t, K, T-t), C(S_t, K, T-t)+Ke^{−r(T-t)}−S_t\}=C(S_t, K, T-t) + max\{...
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1answer
92 views

Pricing a call option with pay-off function max{$S_T - S_{T/2}, 0$}

Pricing a call option with payoff function $C=\max\{S_T - S_{T/2}, 0\}$, where $S_T$ is geometric brownian motion. I appreciate any help! Please close this question if this is a duplicated question. ...
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24 views

CVA quality of regression (Longstaff & Schwartz method.)

I am performing a LSMC (Longstaff Schwartz Monte Carlo) over an american option. I run the regression over the paths I setup, however I would like to check the quality of the regression. Some ...
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1answer
43 views

Approximate Hagan formula for SABR model with negative beta

While looking into fixing the $\beta$ parameter (based the following regression: $\text{ln } \sigma^{ATM}_t = \text{ln } \alpha - (1-\beta)\text{ln }F_t$, as explained in West (2004), page 6) before ...
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2answers
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Why do we need approximation in option pricing?

We know that we can get a closed form for European option price. And we can calculate directly the normal distribution accumulation. But I saw that people use many approximation methods such as ...
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0answers
47 views

Why do we require a continuous volatility calibration while pricing Options [closed]

On pricing Options the volatility surface is represented by a mathematical model (with parameters). What does it mean to calibrate the volatility surface How often has the volatility surface to be ...
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1answer
37 views

Basic Replication of European Call Option

I am looking at the very basics of replicating an option with a portfolio of risky and risk free assets. As such we can define a portfolio of $x$ no. of shares, $y$ bonds & $z$ options at time $(T)...
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1answer
68 views

Usages of variance swap

I’m interested in variance swap. Considered from its feature, variance swap is used for betting the (historical) volatility of underlying asset. If we use it for hedge tool of Vega or Volga, does it ...
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Why futures pricing not calculated like options?

I have read about futures and options ( from online resources ). I only have the basic understanding,not math heavy ( for eg. for Black Scholes I know only the intuitive idea from the khan academy ...
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Calculating historical Volatility for the Black Scholes Model [closed]

Below is a problem from the book "Options, Futures, and other Derivatives" by John C. Hull. I did the problem but I am fairly sure that my answer is wrong. I am hoping that somebody can tell me where ...
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1answer
54 views

Option price of a future

This must be a dumb question. Consider a European option $V$ on a (stock) futures $F$. The hedging condition seems to be the same as that for a stock $$d\Big(V-\frac{\partial V}{\partial F}F\Big)=r\...
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Oscillating errors in finite difference Black Scholes

I am writing an implementation of the explicit finite difference method to price a standard european call option, and comparing the results to the corresponding analytical value to gauge the error ...
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62 views

Basic question about Structured Product Greeks

Say I'm dealing with a structured product (SP): a short put is financing a coupon which is dependent on the paths of the underlying. So typically pricing of an autocall. What's the delta of this ...
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1answer
69 views

Asset price simulation under Monte Carlo for option pricing using market data

I am trying to use Monte Carlo to price some exotic options. I have in mind to simulate asset prices under GBM (say S&P prices) using Monte Carlo and price the option accordingly from the payoffs ...
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27 views

Checking arbitrage for the SABR model - analytical vs numerical approach

I wish to check if the fitted volatility smile/surface from the SABR model for a fixed time period is arbitrage free. Through my research, I've learnt the following need to be checked: The RND (risk ...
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30 views

Delta of an option under assumptions of Bachelier options pricing model

My question is about the computation of deltas under the assumption of a Bachelier pricing model. Am I right in assuming the under the Bachelier options pricing model (with assumption of normal ...
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1answer
57 views

HJM or Short rates model?

When market practitioners do prefer HJM models to short rates models when it comes to pricing derivatives (other than swaptions and caps, let say light exotics to exotics) ? To be more specific, ...
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36 views

Calendar Spread Options (CSO) Pricing Model

I've explored a number of CSO research papers and still cannot comprehend how to effectively use correlation and approximations to price CSOs in crude oil. Can someone please provide some C++ or ...
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2answers
153 views

Interest rates forward implied volatility models

I'm trying to find out which model to use to price a pur forward volatility product named VolBond marketed by structuring desks currently. Let me introduce the products first: Example 1: You pay 100 ...
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154 views

Does Black Scholes need to assume no arbitrage?

Since Girsanov's theorem guarantees a risk neutral measure for Geometric Brownian motion, by the fundamental theorem of asset pricing there can be no arbitrage. So, why does the model assume no ...
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Pricing caplet with Bachelier (normal dynamic) using forward measure

I'm trying to price caplet with Bachelier under forward measure, but I can't find any solution. Remind that Bachelier assumed rates follow a normal dynamic. So here what I was doing : $C_t(T,T+d)$ ...
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1answer
66 views

Using Geometric Brownian Motion for Index Options

As far as I understand, in most of the cases we derive the option valuation assuming that the log-return of the asset is partly driven by its own Brownian motion, and we use Geometric Brownian motion (...
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1answer
54 views

option price change

I am trying to match change in European Call option price to greeks using the calculator here e.g. for S=95, K=100, r=0, V=25, t=5 and dividend=0, I get ...
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Pricing European Call on Coupon Bond in Lattice

What's the best approach to pricing a par call option on a coupon paying bond? Is it to discount the greater of the price and strike through the lattice? And for this, is the price used the dirty or ...
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1answer
65 views

Perpetual Put vs European Put

I am looking at a perpetual put option where the strike price is initially the stock price $K(0)=S(0)$ (i.e. at the money), but the strike price grows at the constant risk-free rate $r$ [i.e. $K(t)=S(...
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50 views

About Fourier-Based Option Pricing

I'm reading the book "Derivatives Analytic with Python" by Dr. Yves Hilpisch, chapter 6 Fourier-Based Option Pricing. From page 98 to page 101, the Lewis(2011) Approach was presented. I could follow ...
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27 views

Probability of touch (option) for security

I read through a few related threads on quant stackExchange. Similarly, I am looking for the probability of a security touching $X$ (strike points away) before an expiry time, $T$. From thread here: ...
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0answers
38 views

AFV Model Implementation for Convertible Bonds

I am reading the original AFV model paper for pricing convertible bonds. https://cs.uwaterloo.ca/~paforsyt/convert.pdf The paper is very technical and I am having trouble finding the actual PDE's to ...
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0answers
81 views

Compo Feature in Asian Option on Futures

I'm pricing an Asian option on futures using Turnbull–Wakeman (other suggestions welcome) where the average is defined as $A _ { t _ { 1 } , t _ { n } } ^ { A , f } = \frac { 1 } { n } \sum _ { i = 1 }...
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Does it make sense to calculate an option price in future (at t+1)?

Often I ask myself whether it makes sense to calculate the price of a Call at t+1 supposing for example that underlying asset does no move i.e. $S_{t+1} = S_{t}$ ...
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23 views

Pricing options with 0 or negative underlying values

I am trying to calculate the value of an option whose underlying is the calendar spread between two months for a commodity (front month Brent vs 2nd month), usually known as a calendar spread option. ...
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1answer
109 views

Option greeks as dollar P&L

If I write the value of an option as O(S, K, T, V), where S is the underlying price, K is the strike, T is the time to expiry and V the implied volatility, how can I compute the dollar amount that I ...
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Black 76, finding current forward price and interest rate for a commodity option

Lets say the commodity in question is gas, flowing everyday for a period of time, and my curve data format is "DataEntryDate, FlowingFrom, FlowingTo". To get the forward price should I find the most ...
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1answer
149 views

Measure theory in quantitative finance

When I read up on stochastic modeling, the use of "measure" comes up a lot. So far I just read the word "measure" as "probabilities" or "distribution" and was able to get away with it when trying to ...
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29 views

how to derive vol curve for cross rate

For example I can get vol curves for two assets, say XAU/USD and XAG/USD for time T, I can calculate their asset correlation, obtain probability dension functions. Is there a proper way to synthesize ...
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How does REG-T apply to non-standard option strategies

I'm trying to estimate the margin impacts from non-standard (e.g. not in the CBOE manual) option strategies. How do the rules apply to things like this: (All European) ...
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Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
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Relation between one touch and binary option

Is there a relation between the price of a one touch option and the price of a binary option? By one touch option, I mean an option that pays off a fixed amount if the price of the underlying is ...
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1answer
86 views

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

I am trying to estimate the intraday ATM volatility in a market where the the strike prices are relatively sparse thus the ATM option may not exist (let's say the closest strike is about 2% away from ...
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Question about derivation of SABR volatility formula in original paper 'Managing Smile Risk' by Hagan et al

I have a question regarding the starting point of the derivation of SABR volatilities formulas in the appendix of the famous paper 'Managing Smile Risk' by Hagan et al. To derive SABR volatility ...
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0answers
58 views

Best Way of Interpreting Black-Scholes Formula [duplicate]

I'm curious to know the best interpretation of the Black-Scholes formula for a European equity call option: $$C(S,t)=S_tN(d_1)-Ke^{-r(T-t)}N(d_2),$$ where $d_1=\frac{1}{\sigma\sqrt{T-t}}\big[\ln(\...
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2answers
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Modeling exercise notice time using lattices?

I am interested in modeling callable (say European) bonds which have a time gap between when the future call exercise is decided and when the call actually occurs (payoff) - say 7 business days. I am ...
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1answer
197 views

Quanto pricing explanation

I have paths generated from Heston, correlation Eq/FX, FX ATM vol but then I'm struggling to find the correct methodology. I tried to adjust the dividend in asset paths from my Heston Monte Carlo by ...
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2answers
187 views

Pricing and hedging fund-linked derivatives

I am looking for info regarding pricing, and hedging (notably vega and delta) of derivatives on funds. Could you please confirm/complete the below information I believe I've understood so far, or ...
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1answer
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Develop a pricing formula for an American digital put option

This problem comes from concepts and practice of mathematical finance by Joshi Chapter 8 problem 9. Develop a pricing formula for an American digital put option Joshi's solution - He states that ...
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Beginner question on Black Scholes

Would you please confirm whether my understanding is correct please? (Sorry a lot of questions...) 1) BS is derived based on the assumption that during an infinitesimal time, we can replicate the ...
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1answer
86 views

Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...