Questions tagged [binary-options]
The binary-options tag has no usage guidance.
52
questions
4
votes
1answer
41 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 ...
1
vote
0answers
41 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 ...
0
votes
0answers
26 views
Arbitrage bounds on volatility of price of binary option?
What are the arbitrage bounds on the volatility of the price of a binary option? If the binary price moves too much (such that it violates the arbitrage bounds) what trades would you actually execute ...
1
vote
1answer
64 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
101 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 ...
3
votes
0answers
227 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
99 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
176 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
599 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
vote
1answer
830 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
93 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 ...
2
votes
2answers
311 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 ...
1
vote
2answers
1k 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
2answers
197 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 ...
1
vote
1answer
86 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
266 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} $$
I have to find the analytical expression for the above.
Since $σ(K)=\...
1
vote
1answer
386 views
Pricing for an Odd Type of Asset or Nothing Option
Trying to derive the pricing function for a derivative on two assets $S^1$ and $S^2$ with the following payoff function:
$$\Phi(S^1_T,S^2_T)=S_T^1 \, \unicode{x1D7D9}\{S_T^2\le K\}$$
where I'm ...
1
vote
1answer
50 views
Payoff of an odd indicator of one stock being greater than another
Suppose $S_t^1$ and $S_t^2$ are two stocks following GBMs and have current value $s_1$ and $s_2$ respectively. How can I explicitly compute the payoff
$$
V(t,s_1,s_2)\triangleq \mathbb{E}\left[
1_{\{...
5
votes
1answer
215 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 ...
1
vote
0answers
656 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
2k 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
517 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 ...
1
vote
0answers
283 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
114 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 ...
1
vote
3answers
92 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
votes
1answer
108 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 ...
1
vote
0answers
254 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
votes
1answer
410 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
83 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
votes
1answer
70 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
vote
1answer
125 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
106 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 ...
1
vote
0answers
2k 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 $\$ ...
6
votes
3answers
307 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}^{*}\...
-1
votes
1answer
522 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:
...
0
votes
1answer
134 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 ?
...
0
votes
1answer
958 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 ...
1
vote
3answers
118 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 ...
2
votes
3answers
586 views
Numerical Solution to BS PDE - Digital Option
Here is a relatively simple question about PDE's pricing.
Assume that we are within the BS framework and moreover that interest rate is zero. The price $V(t,S_t)$ of the digital is known to be $\Phi(...
2
votes
1answer
180 views
Is probability implied by binary FX options risk neutral or real world?
If we consider binary FX options in the market and estimate the market implied probabilities of certain FX rates occurring, would these resulting probabilities be risk neutral or real world?
I hear ...
2
votes
1answer
293 views
Effect of vol smile on risk neutral probability of ITM
I was asked in an interview about how the vol smile affect the price of a binary option, which is essentially the Prob(ITM) under risk neutral measure. My thought is that the implied vol at spot ...
4
votes
1answer
174 views
How to value a Binary Option using market data?
Is there a way to calculate the price of a binary option (i.e., an option that pays out 1 dollar when the stock price hits $x$ amount) using market call/put option prices, forward prices, etc. for a ...
5
votes
4answers
8k views
Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options
The asset-or-nothing European option pays at t = T the value of the stock when
at time T that value exceeds or is equal to the exercise price E, and nothing if
the value of the stock is below E. So, ...
2
votes
2answers
1k views
BInary Option implied volaltility
How is implied vol calculated if the quoted prices are out of the range for any possible volatility? E.g. Current quote on CBOE for options expiring on Aug 16, 2014
...
1
vote
0answers
314 views
Pricing binary options with kernel density estimation
Suppose I have a large enough set of prices of an asset, from which I can extract the following function: $f:T\to\mathcal{D}$, where $T$ is a fixed finite set of time intervals (say, 1 minute, 2 ...
8
votes
5answers
1k views
Does an implied volatility always exist for a binary option?
I'm trying to compute the implied volatility of a binary option but I cannot get some of the strikes to reach a convergent solution using either a Monte Carlo pricing model or an analytical Black ...
1
vote
1answer
252 views
Volatility calculation for intra-day cash-or-nothing call binary option
Firstly, I do not have a quant finance background. This is new to me, and I imagine that this is a basic question for this group.
I am calculating the price of a binary/digital option with closed-...
10
votes
2answers
586 views
Extrapolating implied volatilities to small time
Could anyone please direct me to literature or methods for extrapolating the implied volatility surface towards small expiry? I'm looking to price very short time to expiry binary options (e.g. 5 ...
4
votes
1answer
201 views
Creating a doubling and halving position
I want to create a position that either multiplies with $1+u$ (outcome $U$) or $1-d$ (outcome $D$). The probability of $U$ is denoted by $P(U) = \pi$. The initial value of the position is $V_0$. Given ...
17
votes
1answer
999 views
Probability distribution of maximum value of binary option?
A binary option with payout \$0/\$100 is trading at \$30 with 12 hours to
expiration.
Assuming the underlying follows a geometric Brownian motion (hence volatility remains constant), what ...
