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 ...
Options's user avatar
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1 answer
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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 ...
user67120's user avatar
3 votes
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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}^{...
arni's user avatar
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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 ...
Sinbad The Sailor's user avatar
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1 answer
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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 ...
Rodrigo's user avatar
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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 ...
StochasticNewby's user avatar
13 votes
4 answers
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 ...
apocalypsis's user avatar
1 vote
1 answer
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 ...
StochasticNewby's user avatar
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2 answers
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 ...
jgeoirgnlsfnv's user avatar
4 votes
1 answer
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 $dF$ ...
Hasek's user avatar
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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 ...
justLeito's user avatar
2 votes
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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 ...
Wiles01's user avatar
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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..
xelvet's user avatar
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2 votes
1 answer
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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 ...
Matt's user avatar
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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 ...
Ozee's user avatar
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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, ...
PentiumPro200's user avatar
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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 ...
User2001's user avatar
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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: ...
oskar szarowicz's user avatar
2 votes
1 answer
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 ...
user2520938's user avatar
2 votes
2 answers
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)...
quantumtightening's user avatar
3 votes
2 answers
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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?...
quantumtightening's user avatar
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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 ...
Rodrigo's user avatar
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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 ...
Oliver Mohr Bonometti's user avatar
2 votes
1 answer
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, ...
user_12345's user avatar
1 vote
1 answer
394 views

Basket option value calculation

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 ...
Nick's user avatar
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2 answers
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 ...
user66491's user avatar
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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 ?
CLARA.19's user avatar
1 vote
0 answers
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 ...
Homunculus Reticulli's user avatar
3 votes
0 answers
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 ...
freistil90's user avatar
1 vote
2 answers
604 views

Butterfly price bound independent on underlying distribution

Assuming no fees and interest rate $r=0$%, what is the most you would be willing to pay for a \$103/\$106/\$108 European call fly, regardless of the underlying distribution? Buying the fly in this ...
Mattiatore's user avatar
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1 answer
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Does Black-Scholes imply that the expected return for an asset is fixed as the volatility increases? [closed]

I'm new to this, and just trying to understand what options prices imply about asset growth. I'm looking at the following expression for the underlying asset price in the Black-Scholes model, in ...
fairidox's user avatar
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1 vote
1 answer
353 views

Gamma and Theta of a swaption

For a swaption, I had 2 questions: how would I guage the PnL based on RV vs IV on a swaption? I'm guessing its 0.5 x gamma x (RV^2-IV^2)(or realized variance - implied variance) Not 100% sure on ...
IJUT's user avatar
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2 votes
1 answer
217 views

QuantLib including holiday in option price

I am trying to add a holiday to my calendar in QuantLib such that my option pricing model considers this in pricing where I would expect that the time to expiry should decrease with the inclusion of a ...
pinkusfloyd's user avatar
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Time steps in CRR Binomial Option Pricing for American Options

how do you determine the time steps required as inputs to the Cox Rubinstein Binomial Option Pricing model when trying to determine the fair price of an American option? Most textbooks and literature ...
louis xie's user avatar
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5 votes
2 answers
668 views

Pricing and hedging caps and floors on illiquid emerging markets

I'm tasked with the problem of setting up a cap/floor trading on an emerging market which doesn't have any interest rate derivatives traded yet besides plain vanilla interest rate swaps. We intend to ...
Hasek's user avatar
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0 answers
50 views

What is the meaning of Domestic Exchange Rate here?

So I have the following formula for the Pricing of a Quanto Option (see image below). While I understand this formula pretty well, I am not sure what is referred to as "domestic exchange rate&...
Ozee's user avatar
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3 votes
2 answers
1k views

SABR model - beta

In the SABR model, the parameter beta largely controls the back-bond behaviour of the model. How do people estimate beta? One approach is to regress atm vol vs forward, i.e. $$\ln(\textrm{atm vol}) = \...
JohnRoper's user avatar
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0 answers
64 views

Sticky Strike vs Sticky Delta - revisited [duplicate]

Given a time series of implied volatility smiles over the last 100 days for a given option (e.g. 1y S&P call, or 1y x 10y swaption), and the corresponding forward rates, what test should be ...
JohnRoper's user avatar
1 vote
0 answers
78 views

How can I derive the price of american options given the european options prices? [closed]

I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type?
Rodrigo's user avatar
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3 votes
1 answer
157 views

Volatility model for pricing of Down-In Put options

What is the best volatility model to price Down-In Puts (DIP) under several stress scenarios (e.g downward movement of underlying price by -5%, -10%, -15%)? Please note that I got the market prices ...
Alex Papas's user avatar
3 votes
1 answer
294 views

Right risk free rate to price an Option using BS formula

I understand this is very basic question but I still scramble to determine what would be right risk free rate to price a simple European call option using Black-scholes formula, with maturity is 5 ...
Brian Smith's user avatar
1 vote
0 answers
363 views

Implied volatility to local volatility via Dupire

I am doing some self study on stochastic local volatility modelling and am having a hard time replicating some results from the paper "FX Option Pricing with Stochastic-Local Volatility Model&...
APMATH24's user avatar
0 votes
0 answers
70 views

Characteristic Function Kou (2002) Model

I'm looking for the correct characteristic function for the Kou (2002) jump diffusion model. Can someone help me? Because if I try to look at it online everyone forgot $r$ and $S_0$. This is what I ...
Lucy's user avatar
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0 answers
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Price of financial assets at $t=0$ in Black-Scholes framework

Given the share price equation $$ dS_t=rS_tdt+\sigma S_tdW_t $$ working in the framework of Black-Scholes model, find the price at $t=0$ of the following two financial assets: (a) The asset pays at $t=...
Tyrell's user avatar
  • 101
1 vote
0 answers
79 views

Calibration period

I want to calibrate some model to market data. This could fx be Bates, Kou, Black-Scholes, etc. So, for each model we have a set of parameters which need to be estimated through calibration. Now, my ...
CasMath's user avatar
  • 59
0 votes
1 answer
195 views

Delta of a forward ATM option

Reading: What are some useful approximations to the Black-Scholes formula? I understand that a ATM Call option can be approximated to $$ C(S,t)≈0.4Se^{−r(T−t)}σ \sqrt{T−t}$$ Also, I often hear that an ...
user25844's user avatar
  • 365
2 votes
2 answers
949 views

How to understand wedge?

It is heard that trading wedges (cap/floor straddle - swaption) is actually trading the correlation btw forward rates. How to understand this? Either swaption or cap/floor seem to be insensitive to ...
JUW's user avatar
  • 51
2 votes
1 answer
299 views

How to find IV from market prices accodring to Bergomi

I was conviced to read Bergomis book on stochasic volatility to learn how options are traded in practice. He basically writes that the probabilisitc side is rather useless and that one only uses the ...
Nocturnal's user avatar
2 votes
1 answer
456 views

How is an exchange rate process a martingale under any measure?

Suppose a process for a stock price of a US-based company traded in the USA is, under the USD money-market numeraire: $$dS_t=S_tr_{USD}dt+S_t\sigma_SdW_1(t)$$ Using fundamental theorem of asset ...
Conductor's user avatar
0 votes
0 answers
182 views

Can the break-even of a straddle be lower than the implied move?

Let us consider a two day option: 1 day having a baseline vol of 16% 1 day having an event for which we want to find the implied move, higher than 16% Is it possible that the price of the straddle ...
SaltyBagel00's user avatar

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