Questions tagged [binary-options]

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33 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-...
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2answers
93 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 ...
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2answers
94 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. ...
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3answers
153 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
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1answer
62 views

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 ...
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2answers
195 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 ...
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0answers
71 views

Portfolio of American Binary Option and Knockout Option

Assume I have a portfolio where I long an American Perpetual Binary option (that pays 1 if S>=K and 0 otherwise) and I short a knock out barrier option. This ...
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2answers
160 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 ...
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1answer
66 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: ...
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2answers
127 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 ...
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0answers
84 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 ...
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2answers
111 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 ...
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38 views

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 ...
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1answer
101 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 ...
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0answers
50 views

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 ...
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1answer
127 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.
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0answers
302 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 ...
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0answers
443 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 ...
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1answer
152 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 ...
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0answers
365 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 ...
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1answer
1k 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 ...
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1answer
1k 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 ...
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1answer
160 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 ...
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2answers
746 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 ...
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2answers
3k 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 ...
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2answers
286 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 ...
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1answer
137 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 ...
2
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1answer
395 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)=\...
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1answer
458 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 ...
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1answer
58 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_{\{...
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1answer
238 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 ...
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0answers
888 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)...
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1answer
4k 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 ...
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4answers
735 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 ...
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0answers
329 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&...
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2answers
126 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 ...
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3answers
96 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 ?
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1answer
137 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 ...
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0answers
272 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 ...
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1answer
656 views

Justification for Binary Option's Infinite Delta?

First time poster here. Glad to be here. I just graduated with an MSc in computational finance. I recently read a question by another user about the delta of an at-the-money binary option as it ...
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3answers
91 views

How are bets and high-risk investments conceptually different, and how does this apply to binary options?

They look pretty similar to the layman's eyes: You have to pay something, and then a non-deterministic (or non-fully-known) event occurs. Such event has a (perhaps unknown) probability of occurring ...
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1answer
78 views

Binary Options hedge Forex position

if I am short GBPJPY and it start to jump up, instead of closing it, could I use Binary Options to long it immediately after jump up? So I could hedge current Forex position if possible.
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1answer
147 views

Arbitrage opportunity in discrete time

Say we have the following binary option $B$ on asset $S$ with strike K and expiration time T, assume also that the following relation holds at time $0$: $B > N*C(K,T)-N*C(K+1/N,T)$ Where $N$ is ...
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2answers
113 views

Counting random paths

Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time $t=0$ is 1024. The upstage factor of the stock price is $x=1.25$ and downstage factor of ...
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0answers
3k 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
942 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
592 views

Is the code of my binary call option pricer (using explicit finite difference, backward scheme) correct? [closed]

I am using explicit finite difference (backward scheme) to price a binary call option. Here is my MATLAB code: ...
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1answer
186 views

Binary Option valuation problem in R using RQuantLib; also result validation aspect

When I am trying to value Binary Option using RQuantLib I am not getting all the greeks for exctype "american" wheras "european" exctype is fine. What is the problem here ? ...
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1answer
1k views

Put-Call Parity Arbitrage Exploitation for Binary-Asset-or-Nothing Options

Is the Put-Call-Parity valid for binary (asset-or-nothing) options? If not, is there another formula for such exotic options? I know that for regular options, there are arbitrage opportunities when ...
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3answers
121 views

Is it realistic to assume that the current price of a stock takes into account the probability of it going up or down in the future?

I'm currently reading the following lecture notes: http://www1.maths.leeds.ac.uk/~jitse/math2515/lecture04.pdf On the second page, under the subsection titled "The Risk-Neutral World" it points out ...