Questions tagged [binary-options]

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17
votes
1answer
998 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 ...
12
votes
3answers
6k views

How does volatility affect the price of binary options?

In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
11
votes
6answers
2k views

Do binary options make any sense?

Reading from "www.nadex.com" - the copy reads "Binaries are similar to traditional options but with one key difference: their final settlement value will be 0 or 100. This means your maximum risk and ...
10
votes
2answers
571 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 ...
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 ...
6
votes
3answers
301 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}^{*}\...
5
votes
1answer
212 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 ...
5
votes
4answers
499 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 ...
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 ...
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 ...
4
votes
3answers
7k 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, ...
3
votes
1answer
38 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 ...
3
votes
1answer
98 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 ...
3
votes
1answer
571 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 ...
3
votes
0answers
81 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
205 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 ...
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 ...
2
votes
2answers
289 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
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 ...
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
289 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 ...
2
votes
1answer
258 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)=\...
2
votes
1answer
389 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 ...
2
votes
3answers
582 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
0answers
151 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 ...
1
vote
1answer
374 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
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 ...
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
1answer
790 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
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_{\{...
1
vote
3answers
88 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 ?
1
vote
1answer
59 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.
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
186 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
81 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 ...
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 ...
1
vote
1answer
251 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-...
1
vote
0answers
39 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
vote
0answers
639 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)...
1
vote
0answers
281 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&...
1
vote
0answers
252 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 ...
1
vote
1answer
123 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
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 $\$ ...
1
vote
0answers
311 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 ...
1
vote
1answer
92 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 ...
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 ...
0
votes
1answer
107 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 ...
0
votes
1answer
133 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
69 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.
0
votes
1answer
913 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 ...