Questions tagged [binary-options]
The binary-options tag has no usage guidance.
69
questions
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76 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 ...
-1
votes
2answers
135 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 ...
0
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0answers
39 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 ...
0
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1answer
114 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 ...
0
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1answer
88 views
Option Pricing - Incorrect price outcome for Out of the Money (OTM) calls
I have the options data for a stock -
...
0
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1answer
213 views
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 ...
1
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1answer
108 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-...
1
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2answers
236 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 ...
4
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2answers
210 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. ...
2
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3answers
183 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
1
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1answer
90 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 ...
2
votes
2answers
330 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 ...
0
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2answers
292 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 ...
0
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1answer
105 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:
...
2
votes
2answers
220 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 ...
3
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0answers
94 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 ...
2
votes
2answers
152 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 ...
1
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0answers
46 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 ...
7
votes
1answer
114 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
51 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 ...
1
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1answer
180 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.
3
votes
0answers
502 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
499 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 ...
3
votes
1answer
173 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 ...
2
votes
0answers
432 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 ...
3
votes
1answer
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 ...
1
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1answer
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 ...
1
vote
1answer
191 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 ...
3
votes
2answers
928 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 ...
2
votes
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 ...
1
vote
3answers
387 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 ...
2
votes
1answer
149 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
votes
1answer
435 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)=\...
1
vote
1answer
485 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 ...
1
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1answer
59 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
$$
V(t,s_1,s_2)\triangleq \mathbb{E}\left[
1_{\{...
5
votes
1answer
250 views
How do binary options broker hedge themselves against losses?
My question refers to the fact that, for most part, binary options are basically gambling, but not to the full extent. Due to the advanced models, capital anomalies like Momentum and possibly technial ...
2
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0answers
986 views
Greeks(theta) of a Down-and-Out barrier option
I am trying to figure out the theta for a down-and-out barrier put option. After some research of my own, I found out that a down-and-out put can be expressed as
$$
P_V(S_0, S_0)-P_V(S_0, H)-(S_0 - H)...
2
votes
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 ...
5
votes
4answers
783 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
348 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&...
0
votes
2answers
132 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
101 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 ?
0
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1answer
147 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
289 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 ...
2
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1answer
779 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 ...
1
vote
3answers
92 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 ...
0
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1answer
84 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.
1
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1answer
154 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 ...
1
vote
2answers
121 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 $\$ ...
