Questions about models for the valuation of option contracts.

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Connecting Call price computed discretely to call price computed under continuous time case

I want to connect the call premiums calculated discretely via the binomial pricing method to the Black-Scholes-Merton formula for the call premium which applies to continuous time case. The framework ...
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1answer
44 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
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2answers
165 views

Why is the term structure of the implied volatility surface non-monotonic?

Does this reflect expectations & uncertainty about interest rates (exposure to rho?), event driven concerns about the underlying, or something else?
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1answer
88 views

option time value in the pricing models

option price = intrinsic value + time value where intrinsic value (in other words payoff at N) is defined generally as difference between the underlying asset price and strike price (order depending ...
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3answers
98 views

Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
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59 views

Binary American Call Option (Cash or Nothing)

Suppose we have a stock with current price $S(0)=X$ and the interest rate is zero. When the stock reaches level $\$ H$ for the first time ($H>X$), the option can be exercised and its payoff is $\$ ...
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3answers
81 views

Linear combination of payoffs of bull and bear spreads

Write the following payoffs as linear combination of call options with different strikes and possibly some cash and give the closed form formula for them. Attempted solution: The payoff for the bear ...
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1answer
36 views

Known future volatility and difficulty in predicting final P/L

I have started Chapter 1 of Dynamic Hedging by Taleb and it starts by saying "Even if traders knew the exact future volatility but hedged themselves (rebalanced the gamma) at discretely spaced ...
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1answer
85 views

Lookback option to find stock price

Consider the payoff equation for the lookback option $\psi(T)= max(S_t-S_T)$, where $t\in[0,T]$ and $S_t$ is modeled by the geometric Brownian motion with constant parameters. Find the price of stock ...
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1answer
58 views

A clarification on the Heston option pricing formula

I have carefully reconstructed all the computations that lead to the Heston option pricing formula for a call. I end up with this formula for the "adjusted" probabilities $$ P_j\left(x,v,T;\ln K\...
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40 views

Pricing function $P(S,t)$ is convex in $S$ for all $t$

I am now reading Alternative Characterization of American Put Options by Carr et all (available at http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf). There is a theorem called 'Main ...
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1answer
56 views

Interpolating on the BS parameters and injecting in the BS formula vs interpolating directly on option prices

Let's consider a simple European call option. In practice, the way the Black-Scholes formula is used to price it is by injecting all of the parameters and paying special attention to the volatility ...
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3answers
139 views

Binary Option in B-S model - technical question

I want to price Binary Option in Black-Scholes model. The payoff is of the form $f(S_{T})=I_{\{S_{T}-K>0\}}$. If we assume that $t=0$ this is easy, because then we have $C_{0}=\mathbb{E}^{*}\...
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1answer
53 views

Potential Arbitrage profit or proof problem

So the question asks: Consider 4 following European call and put options with the same maturity time: Call option with strike price $100$ sell for $45$ Call option with strike price $110$ sell for $...
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0answers
53 views

Euler discretization bias, heston model

I am performing option pricing using Heston model and Euler discretization. I'm getting the following result: ...
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0answers
78 views

recent developments in American options?

I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based ...
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3answers
395 views

Historical Volatility vs Implied Volatility Performance in Pricing Options

I consistently read on academic papers, when pricing options, using implied volatility is better than using historical volatility. Because, market is more "forward-looking" and historical data is "...
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2answers
2k views

Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
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1answer
100 views

Why is $N(d_2)$ not needed for hedging?

I'm trying to understand delta hedging. If I sell a plain vanilla call option, in order to delta hedge it, I have to buy delta amount of stocks. What I don't understand is that the BS price of the ...
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2answers
129 views

$E[F_T] = F_0 \ \rightarrow \ \text{or} \ \leftarrow \ p = \frac{1-d}{u-d}$?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to ...
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9answers
2k views

Are there any new Option pricing models?

Back in the mid 90's I used the Black-Scholes Model and the Cox-Ross-Rubenstein (Binomial) Model's to price Options. That was nearly 15 years ago and I was wondering if there are any new models being ...
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105 views

Computation of option vega under CEV

It is easy to define the option vega $\nu=\frac{\partial C}{\partial \sigma}$ under Black Scholes model since volatility is a single quantity. However, under CEV or local volaility model, it is ...
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1answer
153 views

How to use the Black-Scholes formula with LIBOR rates?

I want to price an FX option using the Black-Scholes model, but I don't know the risk free rate, nor the volatility. I only know the LIBOR rates, the strike, and that the expiration day is 87 days ...
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2answers
64 views

How to price jumps in payoffs

I specifically want to know how to model a jump condition while valuing a derivative.Example :- the jumps which are observed in digital product payoffs, or barriers and knockouts. Although a ...
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2answers
390 views

Places to make quant code/tools publicly avaliable

Over the years I have developed several tools - including pricing, optimization and calibration tools - most in VBA, C# and C++ I would like to make them publicly avaliable. Aside from putting up my ...
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1answer
70 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
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55 views

Delta hedge compound option

Delta hedge portfolio should be adjusted from one period to the other, as the ratio changes. How does it work with compound options though? Suppose, I have a put on a call option on a stock, in 2 time ...
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2answers
93 views

Difference in implied volatility calculation

I've been using vollib to calculate IV, but my answers have been different by tenths from other sources like NASDAQ and Yahoo. The answers range +- 0.5, sometimes even more. The inputs are: $S$ (...
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1answer
93 views

Black_scholes formula for a butterfly option

Im wondering if I can apply Black-Scholes formula to valorate a butterfly option, i.e: $$B(T)=Vcall(S(T)-K,0)+Vcall(S(T)-K',0)-2Vcall(S(T)-K'',0)$$ with $K<K''<K'$, just evaluating each call ...
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2answers
93 views

Price of an equity

An equity has a value of 100 Euros, and pay a dividend of 5 Euros in 6 months. The interest rate of 6 months is 5% and the interest rate for 1 year is 6%. I would like to compute the value of the ...
3
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1answer
89 views

Approximation of an option price

The value of an option in the money is 11.50 Euros. The parameters of the market are: -The price of the underlying stock: 81.4 Euros. -The volatility ofthe underlying is : 34.65 % The ...
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2answers
166 views

Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
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1answer
132 views

Example of options that cannot be priced with least-square Monte Carlo

Can you give some example of options that cannot be priced with least-square Monte Carlo? Intuitively, this is any option for which a payoff depends on a previous exercise decision. It's relatively ...
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2answers
323 views

Difference between Closing Price, Last traded price and Settlement Price for option contracts?

What is the difference between Closing price, Last traded price and settlement price ? I got the difference between Closing Price and Settlement price from previous post : The difference between ...
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0answers
72 views

School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
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120 views

Ideas for speeding up greek calculations

My current calculations using the vollib library averages 0.5 seconds. Is there any way to get it faster? Any tips/best practice notes will be helpful. This is for a scripting language such as python....
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1answer
150 views

Question in “Computational Methods in Finance” by Ali Hirsa - Chapter 2: Derivatives Pricing via Transform Techniques"

Reference: "Computational Methods in Finance" by Ali Hirsa - Chapter 2: Derivatives Pricing via Transform Techniques" - Page 37* Background: The author prices call option using the Fourier Transform. ...
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100 views

Analytical solution to the Black-Scholes equation with time-dependent volatility

I am stuck with the following exercise and I would appreciate any help with it. I have to calculate the analytical function for the price of a call option given the following process for the ...
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1answer
87 views

Pricing homogeneous Basket Default Swap

Consider a basket with $K=10$ names. Default times of the names, $\tau_k$, are i.i.d. random variables with distribution $P(\tau_k \leq t) = 1 - e^{-\lambda t}$. Suppose that each name in the basket ...
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1answer
27 views

binomial - parameters at which american option hits early exercise possibility

I am looking for a set of parameters (d,u,r,So,K, N=?) for pricing an american call using binomial where the call hits the early exercise possibility. Do you have any exemplary set?
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52 views

Pricing a vanilla call option with a fixed dividend

I have started a finance course few months ago and am looking for a way to compute the price of a 1-year call option with a fixed dividend paid after 6 months. Using Black and Scholes I know how to ...
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1answer
64 views

completeness of the binomial model - proof

I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...
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1answer
58 views

Martingale correction for Andersen scheme with Interest Rate

I have implemented martingale correction to my Andersen scheme for Heston model, as it is in the paper (page 19-22): http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/...
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98 views

Heston model - Andersen scheme implementation

I would like to implement Andersen scheme for Heston simulation. On the following snipped is my code for generating asset path: ...
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2answers
10k views

How to numerically obtain delta?

The delta in option pricing, also called the hedge ratio, is expressed as the sensitivity of the option price to the underlying price change. The analytical solution for the most common option ...
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3answers
72 views

How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing)

We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ...
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2answers
335 views

Barrier option : Monte carlo simulation

I am trying to price a Down-and-Out Call using Monte Carlo simulation. The problem is that I get the right price for the vanilla option (same price as the analytic formula of Black and Scholes) but I ...
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4answers
213 views

Model Price vs Market Price in terms of Fair Price (Options)

Before I start: Ok, this is something I investigated for a fair amount of time and my question is semi-academic. To simplify, I will introduce the short bit (TLDR) of my question and then lay out ...
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1answer
86 views

Black Scholes Geometric Brownian Motion Option Pricing

I'm doing a past paper for one of my masters modules and I'm stuck on this and I have no idea how to tackle such a thing. It's worth 30% of the exam so would be great if anyone here has any ...
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78 views

Does presence of arbitrage necessarily make all derivatives have zero value?

Spin-off from: Pricing when arbitrage is possible through Negative Probabilities or something else I mean in a theoretical sense: If we have a particular market model with some fancy assumptions such ...