Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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How to interpret the (expected) exposure and CVA of an option or a single share

I have a quick (hopefully simple) question regarding the interpretation of the expected exposure of a call option and a single share. I've done some computations on the formula for the expected ...
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1answer
39 views

Constant Maturity Swap dates and conventions

Let's note $L(t,T_i,T_{i+1})$ the libor rate observed at $t$, fixing at $T_i$ with delivery at $T_{i+1}$. The natural delivery date for this rate is $T_{i+1}$, so a vanilla swap with no pay lag would ...
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1answer
33 views

Difference between modelValue from HestonModelHelper and NPV() from VanillaOption

I am trying to calibrate an Heston model and price vanilla option using Quantlib 1.15 and Python 2.7. I use the following code ...
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47 views

Difference between characteristic function and Fourier transform

I'm struggling to understand the difference between this two functions. I have this condition: $P_j:=\mathbb{Q}(S_T>K):=\frac{1}{2}+\frac{1}{\pi}\int_{0}^{+\infty}Re[\frac{e^{iuK}f_j(u,x,v)}{iu}]\...
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1answer
82 views

What is upper left vol?

First time question, so please let me know if you have feedback for how I am asking. I am reading a market research piece and it makes reference to the performance of "vol, particularly the upper ...
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1answer
53 views

American Put Option Pricing

I am trying to solve a question of American Put Option pricing as below. Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with:...
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1answer
100 views

What is the easiest way to learn Option pricing with PDE?

I was reading about Ito's formula and Girsanov theorem, but I am still struggling to grasp how in reality these are combined to compute the price of an option. What are the main source to understand ...
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85 views

Least Squares Monte Carlo

Could you explain to me in words (no formulas) the concept of the Least Squares Monte Carlo method to price an American style option?
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104 views

A crash course in pricing

I need to refresh all the pricing theory. Is there anything like a crash course with practical and intuitive explanations? I will provide any further information. I am a mathematical engineer. I am ...
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46 views

How underlying asset price variance is connected with time

I'm dealing with option pricing models and there is a statement that says the variance of underlying asset price is propotional with time $𝑉𝑎𝑟(𝑆_{𝑚+1})=𝑆_𝑚^2𝜎^2Δ𝑡$ where $\Delta t = \frac{T}{...
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59 views

How to price the american options using local volatility

I have given with a surface of american option prices $C_{am}(T, K)$. From these american option prices the implied volatility surface is deduced. Now I want to find the local volatility $\sigma(s,t)$...
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40 views

Difference between local volatility and implied volatility [duplicate]

I have read several articles about local volatility and implied volatility, but I am still confused with the difference between the two. Please correct me if I am wrong: Implied volatility is the ...
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46 views

Option when underlying follows an ornstein-uhlenbeck process, or something else

I hope this is not a too basic question, but I am fiddling around a bit with option pricing. I have seen option pricing when the underlying in the most common settings, and the process seems fairly ...
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31 views

Option price with underlying growth rate distinct from discount rate

Consider a European style option. The price equation is $$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS\frac{\partial V}{\partial S} - rV = 0 \tag1$$ ...
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23 views

How to retrieve greeks and IVOL historically for listed options (using Bloomberg)?

Is there a way to get Prices, IVOL and greeks on historic option contracts (eg on the underlying RXM15) on Bloomberg, and follow this particular option with Strike K throughout its lifetime (eg on ...
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14 views

Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
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51 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
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29 views

Pricing call option on bond under CIR model by simulating noncentral chi square distribution

In the original paper of CIR model, there is a pricing formula about call option on bond $$ \begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
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1answer
153 views

Pricing under risk-neutral probabilities for weird derivatives?

I would really appreciate some help to value a weird derivative that I've found in an assignment: $$ X=(S_{T_1}-k)^{+} = \max(S_{T_{1}}-k;0) $$ which expires at time $T_{2}$ and uses the price at ...
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44 views

Why not discount the dividend in the european put lower bound condition?

According to the european put lower bound condition: $ p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$ where $t_0$ is now and $t_2$ is maturity. Say $t_1$ is the dividend release time where $t_0&...
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27 views

Using Non-Risk Neutral (Risk Natural) Parameters to Price Options?

Please correct me if any of my following statements are false. My understanding as to why we use Risk Neutral Analysis is that it makes life easy, and ultimately, allows use to come to a closed form ...
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1answer
84 views

How does the Black Scholes Model Incorporate Log Prices Into Model?

I am still not understanding the link between log prices and how that is incorporated into the BS model. I understand why log(S) is assumed because it makes math easier and it prevents ending prices ...
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1answer
176 views

Forward Start Spread Options

Question: We have a spread option with payoff: $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. At time zero only contract $G$ is available for ...
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1answer
67 views

Longstaff Schwartz algorithm

I am new in finance, I have implemented the Longstaff Schwartz algorithm for pricing american otion - one asset (dimension = 1). My questions : Does this algorithm still efficient for a high ...
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45 views

One Period Binomial Option Valuation Model [closed]

My question here is how is the probability of an up move calculated by $(1+Rf-D)\over(U-D)$ derived where Rf is the risk free rate, D is the down move factor and U represents the up move factor. ...
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1answer
109 views

Why isn't this IV calc correct?

I'm trying to calculate implied volatility for the following put option: Stock price = 185.55 Strike = 180 Option price = 3.00 Days to expire = 63 I've run the ...
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28 views

Negative rates, what is assumed for short caplets to derive implied volatilities on long maturities

I have been looking at Black implied volatility data for caps with the Euribor 6M underlying. With negative rates many of the shorter maturity caps have no listed volatilities, and this I completely ...
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33 views

What adjustments need to be made to Heston model to price futures options? [duplicate]

My understanding for the Black Scholes model is that a few adjustments need to be made so that the BS model can be used to price futures. Hence the Black-76 model. What adjustments, if any, do we ...
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39 views

S. Bossu's Correlation Swaps Model

I am reading Sebastien Bossu's "A new Approach For Modelling and Pricing Correlation Swaps" (link). I am recalling some of the definitions from the paper and would like to understand how to prove one ...
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40 views

Pricing a power barrier option

I wish to price an option with payoff $S_T^2{1_{\left\{ {\mathop {\max }\limits_{0 \le t \le T} {S_t} \ge B} \right\}}}$ in the usual Black Scholes setup with zero interest rate. Now the pricing isn't ...
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67 views

Is there an arbitrage free option model that treats volatility as a deterministic function of strike?

I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
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46 views

Multiple layer Monte Carlo Option pricing

I have simulated 10000 price paths from the SVCJ model under $\mathbb{Q}$ from $S_{t0}$ until $S_{tm}$ and have computed one discounted option price $C_t$. I want to compute the numerical simulated ...
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1answer
67 views

Why do we have to use in-the-money paths in LSMC, and how?

In Longstaff's original LSMC paper (Valuing American Options by Simulation: A Simple Least-Squares Approach, 2001 (link)), it is claimed that one should only use in-the-money paths for regression at ...
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41 views

Free Call Option [duplicate]

Suppose we follow the assumptions of the Black-Scholes Model, including unlimited borrowing, continuous prices, and frictionless markets. For simplicity assume the risk-free rate is 0. In this world, ...
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49 views

General assumptions for var swap replication

I've seen claims that the standard static-hedge for a plain vanilla variance swap holds so long as the underlying doesn't jump, but every derivation I have seen begins by assuming the asset follows a ...
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1answer
53 views

How to get Forward price based on Put-Call parity?

Could you advise how to find a forward price using Call/Put (+Spot and Strike) ? Investodepia says that forward is equal to option's strike based on Put-Call Parity but it seems to me there is a ...
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1answer
38 views

Infinite Binomial Pricing no arbitrage

How to price a contract that pays only 1 at the first stock price drop? The stock follows an infinite binomial with no arbitrage $d<R<u$ condition. So the probability of the price going down is ...
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1answer
190 views

What are some beginner quantitative option trading strategies?

I'm new to quantitative trading, with good knowledge in finance and coding (mainly Python, Java, R, etc). I would like to know if there are any basic quantitative option trading strategies that can ...
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1answer
66 views

Solving for Implied Volatility Vega gets stuck at 0 (Python)

So my goal is to calculate option greeks with as few manual inputs as possible. I managed to get the IV for at the money options but then when I try further OTM strikes my results get completely ...
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1answer
82 views

how to simplify Inflation year-on-year option to Zero-coupon option

Belgrade 2004 paper basically proposes that inflation year-on-year volatilities (and hence yoy options) are basically the spread vols between the Zero-coupon vols from (t0 to T) minus the zero-coupon ...
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1answer
154 views

Pricing a callable bond

I have read the Lehman Brother's paper on OAS which I mostly understand, they outline how to find the OAS for a callable bond of which the formula is effectively (ignoring refinancing costs): Market ...
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35 views

Alternatives to implied or historical volatility for calculating implied correlation

For my thesis, I'm trying to calculate implied correlation values from bivariate options. I train my model on 10 years of returns data, price the options, and then invert Stulz's Formula (basically ...
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1answer
73 views

zero-shift SABR vega and re-calibration of SABR

I have a zero-shifted SABR model, where I need to confirm if the model is generating the calibration and vega's correctly. The underlying model is the standard SABR lognormal (there is normal as well)...
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1answer
156 views

Implied volatility in Monte Carlo models

Suppose I want to get the implied volatility for a given option, whose process does not generate a closed-form formula. In that framework, how is the IV calculated, given the fact that bisection ...
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66 views

Can implied volatility be 0?

I am calculating IV for intraday options and sometimes I am getting the value as "0"? Is that possible? For example: Strike = 26700 PE Fut = 26962.55 Spot = 26902.55, TimeToExpiry = 797340sec. Price ...
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Give the formula for following resulting portfolio process

Consider the continuously sampled a derivative security with payoff function $V(T) = \frac {\int_0^TS(u)du}T -K$ but assume now that the interest rate is $r=0$. Find an initial capital $X(0)$ and a ...
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70 views

Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
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1answer
110 views

Pricing in the Heston Model

The dynamics of the Heston Model is \begin{align*} \frac{dS}{S} & = \lambda \sqrt{\nu} d W^S \\[0.5em] d \nu & = k (1- \nu )dt + \epsilon \sqrt{\nu} dW^\sigma \end{align*} where $\lambda$...
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1answer
75 views

Difference between tree and lattice approach

Is there any difference between the tree and lattice approach for valuing derivatives? I was under the impression that both are the same.
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126 views

Do correlated assets affect the price of a portfolio of derivatives?

I need to compute the value at risk of a given portfolio as an exercise for a class at university but I have trouble understanding how correlated assets affect the price of the portfolio. Could you ...