Questions tagged [binary-options]

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What are the boundary conditions for an up-and-out binary call option of Bermudan type?

I know that an up-and-out binary call option of American type will never knock out if barrier is greater than the strike since the option stops immediately if the stock price touches the strike due to ...
Meraki's user avatar
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how does prediction markets automated market makers work with examples?

I am trying to replicate the prices in prediction markets For example on below manifold calculates, how does new probability and payout estimate changes on manifold or on Futuur example similarly, ...
adam's user avatar
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How to 'price' a binary option as a writer or seller of it?

So, suppose you use calls spread to approximately replicate the payoff and therefore 'hedge' the position of shorting a binary call. Suppose the binary call's time to maturity is 1 month. The ...
Chen Lizi's user avatar
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1 answer
85 views

What is your exposure when you sell a binary option

I recently made a post that was closed right away because it wasn't focused and asked too many questions. In that post, I asked five questions that were related but different. It looks like stack ...
Chen Lizi's user avatar
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616 views

Pricing a Digital Barrier Option using QuantLib in Python [closed]

I'm trying to price a EURUSD digital knockout in QuantLib/Python. Ideally would like to get the same output as this stylized Bloomberg OVML model (OVML EURUSD DIKO 1.0000P B0.9500 01/13/23 N1M). I ...
Trent Maetzold's user avatar
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Units when replicating a digital call with vanilla spread

This is an embarassingly basic question, but in the course of studying windmill adjustment in binary FX options, I unexpectedly got stuck figuring out the correct units. Say we have a domestic binary ...
Othman El Hammouchi's user avatar
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192 views

Difference of digital (binary) option price under normal and log-normal assumption

Here is the question asked in interview: What's is the difference of digital (binary) option price under normal and log-normal assumptions of spot? I think the log normal has fatter right tail than ...
user6703592's user avatar
-1 votes
2 answers
428 views

Why can’t delta’s be used to price double no touch options?

Here is the link to a MATLAB one touch option pricing calculator I used:OT I tried several inputs and I noticed that the one touch option price is approximately twice the delta of an equivalent ...
user_is_anonymous's user avatar
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176 views

Clarity regarding Skew adjustment for binary options

I am reading the section on Skew adjustment for binary options on wikipedia (https://en.wikipedia.org/wiki/Binary_option#Skew) and am trying to get my head around it and gain some intuition. First ...
Oscar's user avatar
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1 answer
655 views

The greeks, vanillas and digitals

Question 1: I know website’s like: https://optioncreator.com/ display the pricing and payoff graphs of regular plain vanilla puts and calls. I would like to know if there is any website that displays ...
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Option Pricing - Incorrect price outcome for Out of the Money (OTM) calls

I have the options data for a stock - ...
Saurabh's user avatar
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1 answer
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Digital and binary put/call options

I'm looking for put-call parity for the call and put digital options, but I don't really know what is digital options and it's difference between ...
Saguro's user avatar
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1 answer
297 views

Reason why a European binary call should be worth half of its American counterpart when driftless and out-of-the-money

Exercise 11 of chapter 8 of Mark Joshi's "The concepts and practice of mathematical finance", asks to compare prices of an American and a European digital (binary) calls when out-of-the-...
Giogre's user avatar
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2 answers
842 views

Pricing binary options

A binary option pays an amount of money if an event takes place and zero otherwise. Binary options are usually used to insure portfolios against large drops in the stock market. On March 25, 2021 the ...
arbitrageandy's user avatar
4 votes
2 answers
563 views

Intuitive explanation for the value of a binary option being lower when volatility skew is positive?

According to the formula for pricing binary options with a volatility skew, it appears that the value of the binary option for a given strike gets lower, the higher the volatility skew at that strike. ...
KD89042's user avatar
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3 answers
275 views

Why do Binary Options have a bad reputation?

Actually, I have no experience with binary options trading but on the internet, I see that people talk about them in a bad way. Why does binary options trading has a bad reputation? Thanks
xyzt's user avatar
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Cash or nothing option question [closed]

I got stuck in one exercise of binary options, it says that I have to consider a stock that does not pay dividends, the current price of the stock is 100, the volatility of it is 20%, the risk-free ...
AlejandroL.g's user avatar
2 votes
2 answers
2k views

Why represent a digital payoff as a call spread

Pricing a digital caplet using Hull White model, which pays: $1$ if $R>K$, $0$ otherwise. Why would you represent the payoff as a call spread, i.e. $$\text{Payoff} = \frac{(R - (K+\epsilon))^+-(R ...
user52092's user avatar
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2 answers
565 views

Issue in Pricing Binary Options using Heaviside Function and QuantLib Python

I am trying to price binary option using MC Simulation and Python QuantLib Library. The price of the option matches with the Analytical Engine. However, I am not sure how to incorporate the Heaviside ...
Desi_Quant's user avatar
0 votes
1 answer
251 views

Price of Binary Option using Explicit Finite Difference Method not matching with closed Form solution

I am trying to price the Binary option using Explicit Finite Difference Method. However, the output is not matching with the closed form solution formula. Here is the code for the same: ...
Desi_Quant's user avatar
2 votes
2 answers
576 views

Binary Option Valuation With Skew

In searching for methods of valuation of Binary options with skew, I have found two formulas which are at odds. I cannot find any other references to this valuation formula. Should Vega be positive ...
MonteCarloSims's user avatar
3 votes
0 answers
106 views

How to monetize ability to predict small stock movements smaller than spread?

For a relatively small subset of stock symbols I have been able to build a model that is able to 20-100 times per day consistently predict whether a stock is going up within the next 2 minutes, being ...
Blue Swan's user avatar
2 votes
2 answers
259 views

A PARADOX? - relationship between risk reversal (slope of vol smile) and digital price

how do we resolve this seeming paradox? lets take GBPUSD now: it has a negative risk reversal, ie putvols > call vols , because traders expect spot to fall, so they are buying puts, pushing their ...
Randor's user avatar
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What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
frazier k's user avatar
7 votes
1 answer
133 views

Show that $\frac{\partial c(t))}{\partial \sigma^2 }>0 \text{ if and only if } S(t)<Xe^{-r(r+\frac{1}{2} \sigma^2 )(T-t)}.$

Statement: if $c(t)$ is the price of the digital cash-or-nothing call option, then direct calculation (under Black-Scholes assumptions) shows that $$\frac{\partial c(t))}{\partial \sigma^2 }>0 ...
Idonknow's user avatar
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1 vote
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Calibration using only strike price

I have a binary option and want to calibrate it's BS pricing model. I only have a series of Strike Price vs the Option price, no knowledge on time to maturity, volatility, risk free rate or the ...
Dhruv Mahajan's user avatar
1 vote
1 answer
349 views

What is the shape of the delta graph of the binary option?

I was wondering what the shape of the graph of the delta or the binary option would be.
alicia's user avatar
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3 votes
0 answers
677 views

Deriving the black-scholes formula for the European asset-or-nothing call option

I would like to find out what boundary/final conditions i should be using to find the formula for a European asset-or-nothing call option, as i feel that is where I'm making my mistake. I've read ...
amir ahun's user avatar
3 votes
2 answers
751 views

Bachelier Pricing Formula for Interest Rate Binary Options

Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
qbodart's user avatar
  • 131
3 votes
1 answer
228 views

Fair value of a binary cash-or-nothing option with a barrier

I want to find the fair value of a European cash-or-nothing option that pays \$1 if $S_t>K$ and $S$ breached the level $M<0<K$, where $S$ is the risk-neutral process $dS_t=\sigma dW_t$. My ...
FunnyBuzer's user avatar
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2 votes
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613 views

Binary Options: convert from "Cash or Nothing" to "Asset or Nothing"

I have a formula that uses Black-Scholes to compute the implied pricing of a "Cash or Nothing" binary option on the price of a currency. The option is priced/traded in the same currency as S, K and ...
Snapula's user avatar
  • 113
5 votes
2 answers
2k views

Black-Scholes pricing of binary options

I'm trying understand something basic about Black-Scholes pricing of binary options. In my example above, the current price is over the strike price. The volatility is extreme but I'm still having ...
Snapula's user avatar
  • 113
2 votes
1 answer
2k views

Black-Scholes for Binary Option

Something is wrong with this python code designed to apply Black Scholes to the price of a binary option (all or nothing, 0 or 100 payout). The results I get here is 0.4512780109614. Which I know ...
Snapula's user avatar
  • 113
2 votes
2 answers
523 views

Relation between one touch and binary option

Is there a relation between the price of a one touch option and the price of a binary option? By one touch option, I mean an option that pays off a fixed amount if the price of the underlying is ...
tstudio's user avatar
  • 21
3 votes
2 answers
1k views

Flaw in the following argument with Binary Options and Skew

A Binary option is ATM and expires tomorrow. If the skew of the vanilla options steepens (left side up, right side down) what happens to the price of the Binary Option. I know that using a ...
Trajan's user avatar
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2 votes
2 answers
5k views

Using a call-spread to hedge a digital option

I have a digital option that pays out \$1M at time $T$ if the price of the underlying stock is higher than \$1300 (with current price ~\$1000) and, obviously, zero otherwise. I am in the Black-Scholes ...
Joe Bloggs's user avatar
1 vote
3 answers
464 views

Double knockout binary pricing?

I'm studying the pricing of a Double-Barrier binary option on the price of $S$. By this I mean an option that pays $X$ at maturity $T$ if the lower ($H1$) or upper barriers ($H2$) are not hit during ...
Aldo Shumway's user avatar
2 votes
1 answer
173 views

Where can I see the bid stack for FX?

In trading FX binary options on brief tenors like 1 hour, I frequently see the FX price bounce right on the expiry boundary, like hourly or 20 minute boundaries. I would like to figure out if these ...
Lars Ericson's user avatar
2 votes
1 answer
559 views

Binary option analytical formula

Given $r=0$, $\sigma(K)=\text{const}$ and: $$ \text{Binary} = \lim_{ε → 0} \frac{(C(K,\sigma (K))-C(K+ε,\sigma(K+ε)))}{ε} $$ I have to find the analytical expression for the above. Since $σ(K)=\...
miababy's user avatar
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1 vote
1 answer
524 views

Pricing for an Odd Type of Asset or Nothing Option

Trying to derive the pricing function for a derivative on two assets $S^1$ and $S^2$ with the following payoff function: $$\Phi(S^1_T,S^2_T)=S_T^1 \, \unicode{x1D7D9}\{S_T^2\le K\}$$ where I'm ...
Archetupon's user avatar
1 vote
1 answer
62 views

Payoff of an odd indicator of one stock being greater than another

Suppose $S_t^1$ and $S_t^2$ are two stocks following GBMs and have current value $s_1$ and $s_2$ respectively. How can I explicitly compute the payoff $$ V(t,s_1,s_2)\triangleq \mathbb{E}\left[ 1_{\{...
ABIM's user avatar
  • 353
5 votes
1 answer
289 views

How do binary options broker hedge themselves against losses?

My question refers to the fact that, for most part, binary options are basically gambling, but not to the full extent. Due to the advanced models, capital anomalies like Momentum and possibly technial ...
Richard's user avatar
  • 115
2 votes
0 answers
1k views

Greeks(theta) of a Down-and-Out barrier option

I am trying to figure out the theta for a down-and-out barrier put option. After some research of my own, I found out that a down-and-out put can be expressed as $$ P_V(S_0, S_0)-P_V(S_0, H)-(S_0 - H)...
Byng's user avatar
  • 85
2 votes
1 answer
5k views

Barrier digital options and pricing

What do you call options which behave like barrier options but for a digital option? That is, given $0 < t < T$, then if $S_t > K_t$, the binary option $B(K_T,T)$ comes into play, i.e. which ...
Tony's user avatar
  • 21
5 votes
4 answers
940 views

Asset-Or-Nothing call option price with skew

I have never seen a formula browsing the web for an asset or nothing option price when skew is accounted for. I am surprised I do not see something for this which should be standard in FX since ...
FinanceGuyThatCantCode's user avatar
1 vote
0 answers
446 views

Risk management for Digital Option at large Bank

Say, an investment bank sell Digital Call Option to its client at strike 100. But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&...
Woraphon T's user avatar
0 votes
2 answers
142 views

Close prices discrepancy between binary.com, google, yahoo and wsj?

My algorithm needs to extract the forex data of the last 48h (hourly) to get the last close price and to calculate the MACD. I use Google Finance api becouse is the only which provides free forex ...
mllamazares's user avatar
1 vote
3 answers
111 views

Computation of limit

In Delta of binary option, I do not see how to prove that the limit of $\partial C_t/\partial S_t$ is equal to $+\infty$ as $t \rightarrow T$. Can someone help ?
Georges's user avatar
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1 answer
170 views

Pricing Secured Barrier Call

A European barrier call with barrier $B = 50$, expiration $T = 31$, and strike $K = 33$ costs $12$. The investor is interested in a product that, unlike this barrier call, offers some protection for ...
QFi's user avatar
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1 vote
0 answers
346 views

Pricing Exotic options

I am stuck at a assignment problem where I have to compute the price of an exotic option. I am given the values the prices of option $C(X;k) = E[max(0,X_T - k)]$ for different strike prices $k$ and ...
stochastic_zeitgeist's user avatar