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Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

2
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2answers
168 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 ...
0
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0answers
45 views

Delta of a Digital option [duplicate]

A digital option with a Stock as the underlying pays 1 if the stock price at maturity is above the strike $S_T>k$ and it pays nothing otherwise. I have computed the value proces to be following: $$...
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0answers
29 views

How to value a convertible bond with a one-time callable option embedded

I'm looking at a product (sold by a bank for 11 dollars) which converts to a share of a separate company after 1 year, but gives the bank the one-time option to call the note back after 6 months (for $...
2
votes
1answer
216 views

Manipulation of VIX

Having finished my reading on CBOE's method of calculating the VIX on out of the money call and put options written on S&P 500,I have a thought about the ability of market making firms to ...
2
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0answers
137 views

Higher Order Greeks

In studying options pricing a while back, I had learned of the higher order sensitivities of of Speed and Color. Speed was the rate at which the gamma changes with the underlying. Color is a ...
2
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0answers
166 views

Pricing of multi strike rainbow options

I am looking at the pricing of a two asset multi strike option in the Black Scholes framework but I am struggling with coming up with a pricing formula. The payoff of the option at maturity is \...
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0answers
31 views

Mathematical difference margin, balance, and equity

whilst margin trading with options, a shorting an option position will immediately add the premium to the balance but not the equity(understandably). How does one then calculate the expect value of ...
-1
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1answer
66 views

transaction costs for day trading options

I want to day trade SPY options by buying at the open and closing the position later in the day, but I need to know approximately how far into the money the contract will have to be for me to break ...
2
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2answers
86 views

Why do we only need to buy or sell stock to hedge when the underlying is close to the strike?

Delta mesure the slope of the digital option.It also provides hedging information. Why do we only need to buy or sell stock to hedge when the underlying is close to the strike?
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0answers
47 views

Why does it not make sense to hedge a long position in an option already in the portfolio?

The meaning of hedging I make sense of is to insure and remove all risk associated to an option. However, in the question below because the portfolio already has the option, the goal is to replicate ...
1
vote
1answer
73 views

option on bond future - any caplet representation out there ?

I'm trying to play with bond-future options. Bond future is a future contract on a basket of bonds. The short-side will deliver the so-called bond cheapest-to-deliver (CTD). A bond-future option is ...
1
vote
1answer
741 views

Pricing a double barrier option using Monte Carlo (C++ & Python code included)

I'm trying to price an option with upper and lower barriers using MC where the payoff is $B_u$ when $S_t > B_u$, $B_l$ when $S_t < B_l$ and $S_t$ when $B_l < S_t < B_u$. I have written ...
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vote
2answers
99 views

Option: payout if you beat index

A stock has a mean and volatility. A stock index has another mean and volatility. What is the value of an option that at time T pays out the stock price at time T if the stock has outperformed the ...
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0answers
42 views

call option exercise

I am stuck in this exercise and do not know how to solve it, maybe someone can help me :) We have a special type of European call, the buyer pays the option price at maturity, but only if the option ...
4
votes
2answers
181 views

Option Valuation

Can Black-Scholes option values be derived via the Capital Asset Pricing Model, without resort to the use of a risk-free portfolio being created from the option and a Delta determined quantity of the ...
0
votes
1answer
115 views

option call question

i have a question regarding a call option exercise i cant get my head around The price of a stock is 100, the continuously compounded risk free rate is 5%. The strike price of an european call option ...
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0answers
58 views

Price futures option via replication

I ran into some difficulties when trying to price a futures option via replication in a simple one-period binomial model. I am quite aware that this is easy with risk-neutral probabilities and ...
0
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1answer
306 views

Can I replicate put option by trading futures?

Very basic question. Imagine I have some BTC (which is a bubble but I can't get rid of), and some money on an account which allows me to hedge with CME BTC futures. The problem is that if bitcoin ...
3
votes
1answer
219 views

Variance of options returns

Let's say we write a standard call option on $S_t$ which pays $Max[0, S_t-K] \,\forall \, t \in T $. Given that $\frac{dS}{S} = \mu \,dt + \sigma \,dW_t$, and, $V_T = (S_T -K)_+$, we can solve this ...
2
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1answer
73 views

If I exercise an option, how is it determined who gets assigned?

Does the option carry with it some identifying information about who wrote it, or is the person who gets assigned determined some other way?
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2answers
371 views

Which barrier option has negative gamma?

As said in my book, there exists a kind of barrier option which has negative gamma. I tried the knock in and knock out option, their gamma are positive. Could anyone provide an example where a barrier ...
0
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0answers
72 views

Model Validation - yield curve

I am provided a yield curve which has been bootstrapped using market rates. We use Hull White model and I need to validate the curve and apply it in pricing caps. Is there a step-by-step process ...
0
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3answers
77 views

Call option with rule to sell at a certain price if an event occurs

I want to value a special type of call option on a stock. It's like a regular european vanilla call, but with the added rule that if a certain event occurs (that is approx 10% probability) then they ...
1
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0answers
38 views

Evaluating contract $D$ where the stock follows the Black Scholes assumption

Ch.7 Mark Joshi Problem 14 A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
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1answer
134 views

Down-Out Call and Vanilla call price

We all know from text books and practice that a knock out call is usually cheaper than a vanilla call option. Economically speaking, this comes from the fact that there is a probability bigger than ...
1
vote
1answer
79 views

Why do traders think about options in terms of volatility? [duplicate]

I hear that in practice, traders quote options prices in terms of volatility. What is this convention, and what is the motivation? How do they think about and manage vega risk?
2
votes
1answer
186 views

European option Vega with respect to expiry and implied volatility

I was told that the Vega of an European option always increases when its time to expiry increases (all else equal). I found this confusing and potentially wrong, but there doesn't seem to be relevant ...
3
votes
4answers
347 views

Why are options contracts traded speculatively when investors could just trade the underlying asset?

I'm currently trying to understand why anyone would trade options contracts speculatively. So far I've found 3 possible reasons: Because the underlying asset cannot be traded directly (i.e. you can't ...
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0answers
40 views

Near-the-money options' range

I basically have one year (2016) of data of vanilla options written on SPX. I was trying to isolate the ATM options, but it is hard to have derivatives having exactly K = S in a given day. For that ...
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votes
1answer
104 views

Data on Options on US-Treasury Futes

I am working on an assignment on the Implied Volatility Surface for the options on US-Treasury futures (ZB, ZN, ZF, etc.). I need data on bid and ask, Imp. Vol, Price of underlying etc. Do you know a ...
1
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0answers
89 views

Constant volatility and risk-free rate assumptions of Black Scholes

I'm studying the risk-neutral derivation of Black-Scholes formula and feel confused about the requirement for the volatility of the underlying asset and the risk-free rate to be constant. It seems ...
-1
votes
1answer
97 views

Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 6 [duplicate]

Suppose a stock allows a geometric Brownian motion in a Black-Scholes world. Develop an expression for the price of an option that pays $S^2 - K$ if $S^2 > K$ and zero otherwise. What PDE will this ...
2
votes
1answer
234 views

Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 4

Let an asset follow a Brownian motion $$dS = \mu dt + \sigma dW$$ with $\mu$ and $\sigma$ constant. The constant interest rate is $r$. What process does $S$ follow in the risk-neutral measure? ...
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0answers
168 views

CDS Option Pricing

I have been struggling to create a pricing model for CDS Options or CDX Options using VBA. There do not seem to be any examples that specifically refer to CDS that I could follow. From my research I ...
0
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2answers
348 views

Is the delta of a binary option the same as the delta for a regular European option?

Assume both options have strike of 100, same time to expo, no dividend, same interest rate, same vol and lets say underlying is trading 95. Do both have the same deltas? I read this and still don't ...
3
votes
0answers
121 views

Option pricing formula for deep in-the/out-of money options?

I am learning option pricing and trying to calculate the call and put price using the Black-Scholes Formula. I have calculated the historical volatility to be 0.232. The formula is gives value close ...
3
votes
1answer
406 views

Garman-Kohlhagen (Black-Scholes) Formula vs. Bloomberg OVML Calculator

I'm trying to price a European call option on USDJPY. We have that $S = 112.79, K = 112.24, \sigma = 6.887\%, r_d = 1.422\%, r_f = -0.519\%, T = 0.25$. My model, based on Black-Scholes, returns the ...
2
votes
1answer
227 views

construct an option portfolio on a single asset that is both Long Gamma and short vega

everyone, I have come across this question. How can we construct a portfolio that is both Long Gamma and short Vega and how do we actually hedge long Gamma/short vega position?
1
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1answer
231 views

Call option Delta

I have an exercise where I need to show that the prices of call options $ C(t,K)=E((S_t-K)^+),t \in [0,T]$ with Strike $K$ for fixed $t$: $$\frac{\partial ^+C(t,K)}{\partial K}=-P(S_t>K).$$ We ...
1
vote
2answers
71 views

What is the convention for option tickers on S&P 500 and VIX?

Can you please explain what are all possible versions of S&P 500 option tickers and VIX option tickers? My options historical data is from 2006 to 2013 and I can see something like VIXAB, VIXAC, ....
8
votes
1answer
245 views

How to price VXX options

VXX is an etf that tracks 30-day constant maturity vix futures. Despite the popularity of the ETF and lots of Google searches I could not find any info on how options on this would be priced. I know ...
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0answers
113 views

Where can I get Currency options historical data?

where can I get historical data for currency options? For most part, google gives me links to binary options and other shady webpages.
2
votes
1answer
2k views

Early exercise of American options

I know this question is considered basic and has been asked millions of times, but I have done my research and there are some points that I just can't understand. For an American call, many ...
1
vote
4answers
354 views

List of ISIN for Options, Swaps, Derivatives?

In pages like isin.org or openfigi you can search by an ISIN and you will get information about the share, bond, fund... However, for options , derivatives the search returns 0 results. Is there a ...
2
votes
1answer
115 views

Price of European calls in Merton's Model

The stock price is modeled by $$S_t = S_0 e^{bt +\sigma B_t + \sum_{k=1}^{N_t} Y_k}$$ with $B_t$ Brownian motion, $Y_k$ iid $N(\mu,\delta^2)$, $N_t$ a Poisson process independent of $(B_t)$ and $Y_k$ ...
1
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1answer
241 views

Valuation of Bermudan option as maximum of relevant European options

Assume I need to price a Bermudan option which can be exercised at following dates: $t_1$, $t_2$, ..., $t_n$. I think that the price of such an option will be maximum of the prices of European options ...
1
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1answer
263 views

Leveraged Permanent Portfolio Using ITM Call Options

The permanent portfolio proposed by Harry Browne has had an excellent track record since the 1970's. It is able to compound at roughly 8% annually with a Sharpe ratio around 0.7. The permanent ...
5
votes
3answers
2k views

What really is Gamma scalping?

How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price $V(t,S)$ at time $t$ and the underlying stock price at $S$...
1
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1answer
203 views

Arbitrage strategies in Rubinstein's binomial tree one-step

Suppose that the current stock price is $S_0=20$ and the call option price with no arbitrage is $c=0.633$. Knowing that the expiry stock price can be $S_T=22$ with call option price $1$ or $S_T=18$ ...
1
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0answers
79 views

Black & Scholes with stochastic interest rate [duplicate]

Consider the following model $$\begin{cases} dS_t=r_tS_tdt+\sigma S_tdW_t, \\ dr_t=adt+\eta dW_t\\ \end{cases} $$ where $W$ is a Brownian motion and $\sigma, a ,b, \eta$ are positive constants. I ...