Questions about models for the valuation of option contracts.

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5
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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 ...
2
votes
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 ...
2
votes
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 ...
33
votes
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 ...
1
vote
0answers
104 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 ...
4
votes
1answer
149 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 ...
1
vote
2answers
63 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 ...
3
votes
2answers
388 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 ...
0
votes
1answer
63 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 !
0
votes
0answers
51 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 ...
3
votes
2answers
92 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: $S$ (...
0
votes
1answer
91 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 ...
0
votes
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
votes
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 ...
0
votes
2answers
156 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 ...
3
votes
1answer
131 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 ...
0
votes
2answers
290 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 ...
1
vote
0answers
70 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 ...
0
votes
0answers
113 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....
3
votes
1answer
135 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. ...
0
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0answers
94 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 ...
2
votes
1answer
86 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 ...
1
vote
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?
0
votes
1answer
51 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 ...
0
votes
1answer
61 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 ...
1
vote
1answer
55 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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0answers
96 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: ...
7
votes
2answers
9k 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 ...
2
votes
3answers
71 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 ...
1
vote
2answers
305 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 ...
3
votes
4answers
197 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 ...
1
vote
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 ...
0
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1answer
76 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 ...
1
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0answers
36 views

Cumulants of variance gamma with stochastic arrival (VGSA) model

The characteristic function of the VGSA model is defined as a specific parameterization of the characteristic function of the CIR (Cox-Ingersol-Ross mean reverting process) time-change: $ \mathbb{E}e^...
0
votes
1answer
109 views

How to calculate confidence interval for option price?

I model option prices for European call using Monte Carlo method. What is the proper way to calculate the confidence interval? A. -> Calculate the payoffs (there will be number of zeros as some ...
1
vote
1answer
69 views

Path Dependent Options - Which choice of model?

Can someone please help elaborate/clarify the below statements? I've heard about them from people but would like to know some more detail behind these statements.. - 1) SABR is not useful in pricing ...
12
votes
8answers
7k views

Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
3
votes
2answers
239 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 ...
6
votes
0answers
196 views

How should option prices differ when using the Heston versus the Black-Scholes model?

I am running Monte Carlo simulations for a European Call using Heston Model and I am trying to compare them with prices calculated using Black-Scholes formula. I am not quite sure if the prices I get ...
6
votes
2answers
660 views

The option values are different from two r package - foptions,rquantlib

The results are very different.I know the code from quantlib and the result of quantlib seem right(close to market price). Is there anyone know why the value from fOptions is so large or fOptions used ...
2
votes
3answers
120 views

Greeks for binary option?

How to derive an analytic formula of greeks for binary option? We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us? Wikipedia states ...
2
votes
2answers
228 views

Pricing options under a specific framework

I have a specific framework in mind and I would like to value options under this framework. I am not sure whether a closed form solution exists or Monte Carlo methods would work. The framework I have ...
1
vote
1answer
31 views

no arbitrage condition for paylater option

a paylater option has the folowing payoff: $(S_{T}-K)_{+}-P1_{S_{T}>K}$. To determine the fee P that the option holder must pay, we must write the non arbitrage condition. Why is it this: $E_{Q}[(...
0
votes
0answers
22 views

Price of call (calibration)

I need to understand how we got this : $\forall i \in I $ $C^{*}_{0}(T_i,K_i)=e^{-rT_i}E[(S_{T_{i}}-K_i)^+|S_0]=e^{-rT_i+X_{T_{i}}}E[(S_{T_{i}}-K_i)^+]$ at How we pass from conditional expecation to ...
1
vote
2answers
123 views

Pricing Forward Start Option with PDE

I am looking for references (books and papers) or suggestions on how to price forward starting calls using a PDE approach typically in the Heston model (In the BS world, the computation is trivial), ...
2
votes
0answers
80 views

Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
2
votes
1answer
592 views

Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
3
votes
3answers
140 views

How to price a path dependent exchange option using?

Assume you have two stocks $S$ and $P$ so that at initial time $t = 0$: $S_0 > P_0$. You bought an option which pays off $S_T - P_T$ as long as $S_t > P_t$ through the time $0 < t < T$. ...
1
vote
2answers
90 views

Fourier Transform

In a notes on "Option Pricing using Fourier Transform": Price of plain vanila call is given by $$ C(t, S_t) = e^{-rT}\mathbb{E}^{\mathbb{Q}}[(S_T -K)^+|\mathcal{F}_0] = e^{-rT} \int_K^{\infty} (S_T -K)...
0
votes
1answer
46 views

Swaption on a swap with 0 year tenor

Any ideas on valuation of IRS swaption on a swap with 0 year tenor? As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...