Questions about models for the valuation of option contracts.

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binary option gap option cash or nothing option

i have a lot of problem in understanding binary option specially the gap option how the pay-off can be negative ?and the prime can be also negative how we choose the strik price and the montant cash ...
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Pricing options using particle swarm optimization (PSO)

I am currently trying to recreate some of the work done to price various types of options using particle swarm optimization. In particular, I am trying to price European options using a similar method ...
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4answers
198 views

How do you check your option calculations?

I'm implementing a bunch of different algorithms to price options/find Greeks: finite difference, Monte Carlo, binomial... I'm not really sure how to check my calculations. I tried using QuantLib to ...
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22 views

volatility of a mid curve option

Question: When checking the volatility surface for, let's say, a swaption, where the the option expires in 1Y and the underlying starts in 1Y and ends in 5Y, one would check the volatility surface ...
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22 views

Acceptable difference of Bermudan Swaption prices computed under 1 Factor Hull-White and Libor Market Model

What is an acceptable difference between the Bermudan swaption prices computed with the 1 factor Hull-White model and the Libor Market model? Details: The set of underlying calibration ...
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2answers
63 views

FTAP wih Heston Model

The Fundamental Theorem of Asset Pricing (FTAP) is invoked when we say the time $0$ price of a European option with payoff $g$ is $e^{-rT}E_Q(g(S_T))$, with the hypothesis that $e^{-rt}S_t$ is a $Q$-...
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Can the concept of negative probabilities be used to price a call option?

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
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2answers
249 views

Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
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1answer
47 views

Is Poisson Disk Sampling an alternative to crude Monte Carlo and QMC?

I recently stumbled over Poisson Disk Sampling (here and the meditative version). I wonder if it is an alternative to crude or quasi Monte Carlo for very high dimensional integrals. It is not ...
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1answer
110 views

How does one calibrate a stochastic volatility model?

I will try to use SABR Model to price call options in FX market. What does it mean to calibrate the model? As far as my understanding of the Wikipedia article goes, it means to estimate the parameters....
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1answer
48 views

Pricing of convertible bonds

I'm trying to evaluate a convertible bond using the structural approach : the price of convertible bond is an option (call) on the firm value. We suppose that the firm value is equal to the sum of the ...
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1answer
42 views

Pricing of a Forward-start option in a Black-Scholes framework

I have read the pricing procedure of a Forward-start option in a Black-Scholes world in Musiela-Rutkowski, but I don't find their proof clear (pp. 195-6). Let me summarize their argument: Consider ...
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What does (a,b,c curve coefficients) mean for an Implied Volatility Parameterized Surface data? [closed]

I have a dataset which provides a, b, c curve coefficients for an Implied Volatility Parameterized Surface data for a ticker. What do they mean?
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22 views

How to calculate implied borrow rates from option chain information?

I am given information about a ticker with following options data: stock price, date, expiration date, strike price, call / put indicator, style (American or European), ask price, bid price, mean ...
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2answers
102 views

why Implied Vol (VIX) increase with decrease in Stock Price or vice versa?

why Implied Vol (VIX) increase with decrease in Stock Price or vice versa? whereas Vega is positively related with change in option price to change in stock price.
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Finding the corresponding Strike

I have been asked the following question recently, and I was unable to find the solution (I have the feeling that either a data is missing or I misunderstand a notion). Here is the following question :...
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1answer
58 views

Swaption pricing

I am trying to understand the pricing of various types of swaptions. Suppose I have a swap that starts in 3 months time. How would I go about pricing a swaption on this swap in the following cases: ...
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1answer
77 views

Importance Sampling for Least Square Monte Carlo

I am currently trying to implement and model an Importance Sampling estimator for Longstaff and Schwartz algorithm for pricing American put options. It is used such that more paths are in-the-money ...
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2answers
106 views

Numerical computation of Heston model Integral: Simpsone Rule or Gauss-Legendre Method

I want to price a call option using the Heston model for a given set of parameters. theory from URL: http://elis.sigmath.es.osaka-u.ac.jp/research/Heston-original.pdf The integral equation (18) ...
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2answers
63 views

Black scholes model for down and out European call option using Monte Carlo

I tried to implement Matlab program computing the price of the European down and out call option using Monte Carlo and Euler discretization scheme. I have initial price S0=50, strike K=50, barrier ...
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15 views

HN-GARCH Option Pricing Function produces negative values (fOptions HNGOption)

I have implemented the fOptions package's hngarchFit() function to fit a Heston-Nandi GARCH model to a set of option prices, followed by the HNGOption() function to price them. Unfortunately, the ...
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1answer
54 views

Initial/Boundary Conditions for a Butterfly Option?

What are the initial and boundary conditions for a Butterfly Option? I want to write up a PDE program for it and I have a rough idea of what the payoff should be (is it just a call and a put at the ...
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1answer
316 views

A question about pricing convertible bond with two different underlying assets

I have a question regarding the pricing of convertible bond. If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the ...
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30 views

Is there any literature on a closed-form/analytical solution for American option prices with use of Chaos Theory?

I found the following paper which uses homotopy analysis for a closed-form solution. Does it have direct/apparent connections with chaos theory? http://bfi.cl/assets/zhao-wong-2006---a-closed-form-...
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1answer
421 views

Which distribution do I get?

Let's assume the stock moves according to a classic Black-Scholes model, and makes a proportional jump with an unknown proportion. Say, it is either +1% or -3% of the stock value, and we know for sure ...
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1answer
153 views

Delta of an option derived from the binomial model

I have the following function $V=V(S,t)$, $V^- = V(vS,t+\delta t)$, $V^+ = V(uS, t +\delta t)$. The book proceeds to explain that if we use Taylor series expansion on the above we will confirm that $\...
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1answer
49 views

Pricing Barrier Options with Rebates

How are rebates factored into the Black-Scholes analytical solutions to pricing barrier options? In Hull's book, he does not have rebates factored into the formulas. Can someone point me to a paper ...
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1answer
249 views

Hedging - calculating option prices using implied volatility surface

To hedge a strategy is it accurate "enough" to price an option using an implied vol curve vs moneyness (strike/spot) assuming sticky delta? The moneyness can be read off the chart, its corresponding ...
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1answer
141 views

Complicated American style option contract with numerous non-standard features (simultanous exercise, additional premium, etc.)

I want to value the following contract for times $0<t<T$, i.e. determine $V(t,\cdot)$ where $\cdot$ refers to all other dependences (strike, spot, volatility, etc.). The contract is long and ...
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1answer
120 views

How to price this basket option?

Underlying assets are three global stock index : Eurostoxx 50, HSI, KOSPI 200 Maturity: 36 months with advanced redemption date in every 6 months if prices of indexes satisfy given conditions at each ...
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2answers
363 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
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29 views

How can I improve the pricing simulation of basket option?

I valuated the price of below basket option Underlying assets are three global stock index : Eurostoxx 50, S&P500, KOSPI 200 Maturity: 36 months with advanced redemption date in every 6 months ...
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1answer
76 views

Portfolio with a certain pay-off curve

I would like to find a relevant optimization option's portfolio models which can describe a certain pay-off curve (objective function) under same assumptions. For example, assumptions on how to limit ...
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3answers
1k views

What does “convergence” in Monte Carlo simulation mean?

I have read about convergence in terms of MC simulation for derivative pricing, but I am not clear on what it exactly means. Let us suppose I price an option 100,000 paths twice and both result in the ...
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3answers
189 views

Calculating historical implied volatility

I know that each individual option has it's own implied volatility, but how do you go about calculating the overall implied volatility for an underlying? For example when someone sais the IV of a ...
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1answer
70 views

Expected option return in MATLAB

The expected return of an option is given by its expected payoff under $P$ over its market price under $Q$. For the Black-Scholes model, expected call option return is given as (see here): $$ E(R)=\...
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1answer
21 views

Reference for option pricing, binomial multi-period model using martingales and conditional expectations

The title basically says it all. I am looking for a reference text on the pricing of options in a binomial multi-period model. It should be mathemathically rigorous using martingales and conditional ...
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1answer
139 views

Monte Carlo and PDE results are different for a Call Option!

Okay so this might be a fairly trivial question but I'm having an issue with valuing a call option using both a Monte Carlo method and a PDE method. When I started I first used the parameters: Spot =...
3
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1answer
72 views

How does financial institutions value European options in practice?

I am a little bit confused, or uninformed more truthfully, regarding how option pricing (Europeans only in this case) are handled in real life. Up to now I have acquired some theoretical knowledge of ...
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4answers
381 views

How to price an exchange option using B&S framework?

Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion: $$dX_t= \mu X_t dt+ \sigma X_tdW_t$$ $$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$ Supposing the market is ...
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2answers
88 views

Importance Sampling for pricing options with longstaff and schwartz

I have been asking this similar question before. However, I really want to be concrete and get and concrete explanation. I have been reading the paper by Moreni and try to implement the same ...
3
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1answer
74 views

Implementation of an option tail-hedging strategy

This question directly refers to the paper "Capital Asset Pricing Mistakes: The Consistent Opportunities in Tail Hedged Equities", http://www.universa.net/Universa_SpitznagelResearch_201501.pdf. Very ...
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2answers
119 views

Solution for american perpetual put

I have been attempting an exercise in which I have to determine the value of an american perpetual put, $P$ in terms of the asset value $S$. The solution to the exercise says: When $S>S_f$ (the ...
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Use of real-world probabilities in options pricing: binary event with continuous effect

Let's say I have to price options on instrument X with a multitude of strikes. For simplicity, assume that X only makes one move during the options' lifetime, and this move is affected by some binary "...
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312 views

Derivation of Stochastic Vol PDE

A couple questions regarding stochastic vol PDE derivation. Following Gatheral, a general stochastic vol model is given by \begin{align*} dS(t) & = \mu(t) S(t) dt + \sqrt{v(t)}S(t) dW_1, \\ dv(t) ...
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2answers
95 views

Option pricing, origin of formula $\Pi( t,X)= E^{\mathbb{Q}}\left[e^{-\int_{t}^{T}r_s\,ds} X| \mathcal{F}_t\right]$

Imagine a model with stock prices and dividends of these stocks, as well as a market bond with associated short rate process. It is known that this model is arbitrage-free if there exists an ...
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2answers
152 views

Is it possible that under Black-Scholes: $\ln S_{T} \sim N \left ( \ln S_t - \frac{1}{2}\sigma^2(T-t), \sigma^2(T-t) \right )$

I have a slide on which there is written that under Black-Scholes model: $$\ln S_{T} \sim N \left ( \ln S_t - \frac{1}{2}\sigma^2(T-t), \sigma^2(T-t) \right )$$ Now, here there is a good explanation ...
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1answer
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Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)

According to Duffie, Pan and Singleton (2000) for any real number $y$ and any $a$ and $b \in \mathbb{R}^n$, the price of a security that pays $\exp(aX_t)$ at time $T$ in the event that $bX_t \leq y$ ...
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2answers
55 views

Price and constant hedging portfolio for straddle: $X=|S(T)-K|$

wondering if somebody could check my answer for a homework question! Given a straddle, characterized by its pay-off at maturity $X=|S(T)-K|$, I am asked to find the price of the (simple) claim at any ...
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38 views