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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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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21 views

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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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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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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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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34 views

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
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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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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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
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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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
119 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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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
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 =...
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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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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 ...
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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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37 views

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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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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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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1answer
35 views

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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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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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

Could someone please share the Matlab code for the stochastic volatility jump diffusion option pricing model? (Bates model) [closed]

I have not been able to write a Matlab code for the Bates model without errors. Could someone share theirs please?
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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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35 views

A question on option pricing [closed]

Calculate the value of 9-month American call option to buy 1 million units of a foreign currency using a three-step binomial tree. The current exchange rate is 0.79 and the strike price is 0.80 (both ...
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28 views

Replicating portfolio: initial portfolio?

I have a bit of trouble understanding how to determine the replicating portfolio of a call using just a stock and the riskfree asset. I have times $t = 0,1,2$, and at time $2$, we have $3$ payoffs ($...
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1answer
75 views

What models / methods are used in practice in derivative pricing?

I wrote my bachelor thesis about European Option Pricing under Stochastic Volatility and Jump Diffusion and am now near the end of my MSc in Quant Finance. As i want to write a "potential job"-...
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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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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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2answers
80 views

How is the fundamental theorem of asset pricing used?

I know that a multi-period market model is complete and arbitrage free if there's a unique equivalent martingale measure. The thing is, I have absolutely no clue how to apply this theorem to a simple ...
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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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30 views

Is $(1,0,0,0,…,0)$ a legitimate dividend stream?

A book I am reading defines a positive linear functional as a "price functional" from a set of adapted processes to the real numbers. Specifically, it defines a "consistent price functional" as one ...
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39 views

Option based approach to real capital structures

Has anyone made a serious attempt to apply option theory to real assets and capital structures, taking into account all the messy details ?
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34 views

Estimate Option Price Given X% Move N Days in the Future

I was wondering if someone could recommend a method to estimate the price of an option N days from now given an X% move in the underlying. I have fitted a volatility surface but where I am running ...
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1answer
40 views

Does a Call Spread always need to be symmetric?

I have a plot of a Call Spread Option at time $t ={0}$ but the graph of the call spread is not completely symmetric. My question is: does it have to be? Here is the plot I'm referring to: I'm just ...
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46 views

Comparison of Implied Vol Models

My goal is to evaluate a collection of implied volatility models for accuracy supporting real time theoretical pricing of listed equity option. My current research approach is to define a set of ...
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1answer
82 views

Carr-Madan european contingent claim payoff decomposition formula - application

Looking for some clarification to the values of the parameters used in the Carr-Madan payoff decomposition formula. $$f(S_T)=f(\kappa) + f'(\kappa) (S_T - \kappa) + \int_0^{\kappa} f''(K) (K-S_T)^+ ...
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1answer
118 views

Boundary Conditions for Call Spread

I was just wondering if someone could verify whether these are the two boundary conditions for a Call Spread Black-Scholes PDE. The first one I have is: $max(S_{T} - K_{1}, 0) - max(S_{T}-K_{2},0)$ ...
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71 views

Is this formula correct to estimate a knock out option price using monte-carlo?

I have a knock-out option with barrier $L>0$ and strike $K$ that pays at maturity $(S-K)_+$. So, positive payoff occurs only in case the price stays below the barrier over life of the option. I am ...
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1answer
144 views

Pricing a log-contract using Monte Carlo

Having a payoff of log-contract defined as $$ \Pi_T = \ln \left(\frac{S_T}{S_0} \right) $$ How would you express the MC-estimator for the price of this contract? The stock price dynamics here is ...
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19 views

Pricing with-profit/smoothed bonus annuity using Black-Scholes

Would this be possible? Subsequently, would the pricing of such an annuity be somewhat similar to pricing a lookback option?