A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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9 views

Price Barrier Options on Baskets using Quantlib

Is it possible to price barrier options on a basket of stocks using Quantlib, e.g. a Worst-of Down-and-in-Put on a basket of 3 stocks? I already checked the ...
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0answers
10 views

Options order “logs” - how is it named? And is it somewhere online? [duplicate]

I try to find somewhere "logs" of options orders. I mean - when which order was posted for which option and what size. AFAIK, it is named "ticker tape" for stocks; or level-2.. But is there such ...
2
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1answer
43 views

Implied Vol in Different Payoffs

Let's say I have a black box stock price model I run Monte Carlo on to estimate European call prices. For a given strike $K$ and expiration $T$, I then back out the Black-Scholes implied volatility $\...
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1answer
76 views

Can someone check this boundary condition for me?

At the moment I'm comparing plots between the implicit numerical Black-Scholes PDE and the Monte-Carlo Method for the Black-Scholes equation. However, for the particular boundary condition I'm using I'...
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1answer
73 views

Time Value of Option

I am working on time value of option, and especially with dividend, and I have the following questions. First if the consider the Black Scholes models with no dividends and free interest rate $r = 0$ ...
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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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17 views

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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24 views

Can someone try this Boundary Condition for the Black-Scholes PDE out for me?

I have a bit of a favor to ask and if anyone could help me out with this I'd really appreciate it. At the moment I'm trying to use the triangle wave formula as the payoff for the Black-Scholes PDE i.e....
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1answer
26 views

Variability of IVs of OTM options

I'm attempting to fit a curve through moneyness/IV datapoints of intra-day options. As you can see, the data gets sparser and more variable for highly OTM options. I'd like to argue why the outliers ...
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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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0answers
21 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
55 views

Black-Scholes PDE boundary condition question regarding limits

I'm working with the Black-Scholes PDE and I'm testing some things out by taking an initial condition for it as $\sin(S/50)$, where $S$ is the spot price. My issue comes with attempting to find the ...
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0answers
35 views

Calculation of option Greek (sensitiviety) theta via finite difference

I am able to get good approximations for delta, gamma, and rho via finite difference method, but not theta. I believe my issue is the value of h. Theta is basically the difference between the price ...
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1answer
124 views

What is the probability that a OU process hits an upper barrier U before a lower barrier L?

What is the probability that the arithmetic OU process $dx_t= \theta(\mu-x_t)dt+\sigma dW_t$ hits barrier $U$ before hitting barrier $L$ when $L<x_0<U$ ?
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3answers
112 views

Heston Model Integration Oscillations

Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
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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
72 views

Why buy/sell a forward starting option?

More precisely, in equity markets, why would one prefer to buy a forward starting option over a vanilla option ? What about the selling side ?
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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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97 views

Do Options and Other Derivatives follow any mathematical laws?

I'm interested in abstracting out some properties of options and other derivatives for software library I am implementing. I was wondering if options follow any sort of mathematical laws, for example, ...
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2answers
58 views

How to replicate a correlation swap using only vanilla options and underlying

Assume I have two assets A and B that are positively correlated most of the time. I'm trading a strategy based on this correlation. Is there a way to protect myself in the event that the correlation ...
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1answer
63 views

Writing an Options Strategy Backtester

I've been doing some digging, and this question has been asked many times in various forms over the years - Backtesting Options Strategies in R Are there any good tools for backtesting options ...
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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)=\...
3
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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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1answer
65 views

How do I calculate the probability of a short option position expiring worthless?

I want to be able to determine the probability of a short option position (call or put) expiring worthless. Don't know where to start but I see probabilities derived from the greeks on some web sites?...
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1answer
121 views

Probability of Brownian motion particle touching barrier given path starts at $X_0$ and ends at a known $X_t$

I have been reading Su and Rieger's paper on barriers and from there have been able to work out the unconditional probability of the process $dXt = μ dt + σ dWt$ touching a down barrier $α$ to be $\...
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1answer
48 views

How should I understand expiration dates?

The following is an excerpt from Introduction to the Mathematics of Finance by Roman: Expiration Dates The last trading day of an option is the third Friday of the expiration month and the ...
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1answer
49 views

Implied Expected Stock Return from European Option Prices

We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as: $$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$ The result is ...
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1answer
109 views

How to derive an option price for an asset with these dynamics?

Assuming my underline asset price follows the process: $$d\ln (F_{t,T})=-(1/2)\sigma ^2e^{-2\lambda(T-t)}dt+\sigma e^{-\lambda(T-t)}dB_t $$ How should I derive an option price formula?
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2answers
76 views

How is the Chooser Option's value computed in this example?

In preparation for my finals, I am attempting a question on chooser options. One question asks A European chooser option on an index ETF paying a yield of 3.0% with strike \$64 has a maturity of ...
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2answers
120 views

Carr-Madan Formula

Really new to financial Maths. I am currently having problems with the Carr-Madan Formula. $$f(S_T)=f(F_t) + f'(F_t) (S_T - F_t) + \int_0^{F_t} f''(K) (K-S_T)^+ \ d K + \int_{F_t}^{\infty} f''(K)...
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1answer
82 views

How to understand this example from Hull's book?

I just started reading Hull's book, and I got stuck in an example where a financial institution has sold for $300,000 a European call option on 100,000 shares of a non-dividend-paying stock. Stock ...
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2answers
56 views

Why would one prefer variance swaps over other instruments?

I understand that an investor who has a view on an underlying's variance would be tempted by a variance swap. But why would one prefer such a contract over another instrument whose value is based on ...
3
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1answer
53 views

Deep ITM Call Implied Vol via Monte Carlo

Let's say I've computed the price of a call using Monte Carlo with $S_0 = 100$ and $K = 80$, using $T = 0.1$ and $r = 0$ to be $\$20.00095$. This price estimate comes with a $95\%$ confidence ...
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4answers
189 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 ...
2
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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
62 views

construct volatility smile based on historic observations

So I calculated historic volatility/skewness/kurtosis for a commodity. I now would like to construct a volatility smile that reflects this historically realized distribution. I tried using some ...
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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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0answers
47 views

How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model

Here are two questions related to implied volatilities. a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also ...
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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
58 views

Delta Hedge, does large stock move produce a loss?

I dont understand how MM protect themselves from large moves in underlying while being delta hedged. Example: MM sels 1 ATM put and sells 100stock (delta = 1) as a hedge. Now what will happen if next ...
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1answer
44 views

Special term for 'intersection' of option price

Suppose, I have written two ordered lists: $S_{call}= (\textbf{8000, 8050, 8100}, 8150, 8200, 8250)$ and $S_{put} = (7850, 7900, 7950, \textbf{8000, 8050, 8100})$. Entities are correspond to strike ...
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2answers
41 views

In an example of “call options”

The following is an excerpt from Introduction to the Mathematics of Finance by Roman: As a more concrete example, suppose that IBM is selling for $\$100$ per share at this moment. A $3$ month ...
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35 views

Is it possible to place hidden order inside spread when trading E-mini S&P 500?

My question is not about hidden orders in general. In equity market a trader can post his hidden order inside spread, is it the same way for E-mini S&P 500?
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2answers
407 views

How to derive the price of a square-or-nothing call option?

At maturity $T$, the holder of a "square-or-nothing" call option written on an underlying $S_t$ receives a payoff of the form $$ \phi(S_T) = \frac{S_T^2}{K} \pmb{1}_{\{S_T \geq K\}} = \begin{cases}\...
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1answer
85 views

Is This A Viable Alternative Options Pricing Method?

i'm currently a high school student who hasn't gone past Algebra II, and thus I have minimal Calculus knowledge. I know the basics of Integration and Derivation (drop the coefficient, raise to the ...
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0answers
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
57 views

Why is H always* the letter used to describe the level of a barrier?

A quick and (hopefully) easy question. Why? *(always / often / when it's not B)
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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 ...