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.
15
votes
5answers
2k views
Skew arbitrage: How can you realize the skewness of the underlying?
It's not clear to me how to realize skewness. In other words, how do you implement skew arbitrage? There seems to be no well-known recipe like in volatility arbitrage.
Volatility arbitrage (or ...
2
votes
2answers
536 views
How to Delta Hedge with Futures?
The theory of delta hedging a short position in an option is based on trades in the stock and cash. I.e. I get the option premium and take positions in the stock and cash.
In the classical ...
3
votes
2answers
276 views
Why do ATM call options have a delta of slightly bigger than 0.5 and not 0.5 exactly?
From the formula of the delta of a call option, i.e. $N(d1)$, where $d_1 = \frac{\mathrm{ln}\frac{S(t)}{K} + (r + 0.5\sigma^2)(T-t)}{\sigma\sqrt{T-t}}$, the delta of an ATM spot call option is ...
1
vote
0answers
82 views
Pricing a Power Contract derivative security
I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
12
votes
6answers
665 views
Setting the r in put-call parity?
Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$.
The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification.
The variable $r$ is ...
7
votes
2answers
403 views
When does delta hedging result in more risk?
There's a question in an interview book saying "when can hedging an options position make you take on more risk?"
The answer provided is that "Hedging can increase your risk if you are forced to both ...
1
vote
0answers
81 views
How to calculate a the PFE for a Swaption?
How do you calculate the Potential Future Exposure (PFE) for a swaption?
Do you incorporate the dynamics of implied volatility when you are running your simulations?
Is there a standard way to ...
0
votes
0answers
152 views
Lagging Beta Strategy
Came across a method involving pairs in the book Hedge Fund Market Wizard:
Given a Stock(or Collective of instruments)that follows closely to say Dow index with a beta<1(very short term) but ...
2
votes
1answer
69 views
Question on OptionMetrics: when are adjustments for discrete dividends needed?
Bakshi et. al. (1997) analyzes the empirical performance of some alternative option pricing models. I am interested to do this as well - hence applying different models - but I am unsure how to handle ...
-4
votes
1answer
135 views
Show that convexity of call price as a function of the strike is violated [closed]
European call options with strikes 90, 100 and 110 on the same underlying asset and with the same maturity are trading for 22.50, 18.84 and 13.97 respectively. show that the convexity of the call ...
6
votes
4answers
477 views
Why the interest rate for put-call parity is not constant?
Usimg the put-call parity
$C - P = S - K ยท e^{-rt}$
I tried to estimate the value of $e^{-rt}$, the present value of a zero-coupon bond that matures to 1 in time $t$:
$e^{-rt} = (P - C + S) / K$
...
3
votes
1answer
167 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 ...
3
votes
2answers
306 views
Equity option portfolio greeks with underlying
I'm curious about how to construct the five basic greeks for an equity option portfolio when there are shares of the underlying in the portfolio.
For example, a portfolio of 100 call options and 100 ...
3
votes
2answers
122 views
self-consistent parametric form for equity implied volatility
I recall reading a paper, but can't remember where I found it. In short, there was a parametric form for volatility smile/skew that fit both index and single stock vol slices and had intuitive ...
10
votes
7answers
2k views
Why does implied volatility show an inverse relation with strike price when examining option chains?
When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts.
As a current ...
6
votes
2answers
343 views
How to transform process to risk-neutral measure for Monte Carlo option pricing?
I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is ...
3
votes
1answer
121 views
How do I model risks for specific short-term short calls in a portfolio with limited data?
I'm trying to do some risk analysis on a portfolio of bonds, currency, stocks and short calls. The short calls expire in approximately 15-30 days and I've only got around 20 days of pricing data on ...
2
votes
1answer
140 views
Greeks and Option Premium
If a linear sum of options is constructed such that the premium payout is zero, then does it mean that resultant greeks of the cumulated options positions will be nearly zero. For simplicity, lets ...
7
votes
2answers
459 views
When to use Monte Carlo simulation over analytical methods for options pricing?
I've been using Monte Carlo simulation (MC) for pricing vanilla options with non-lognormal underlyings returns.
I'm tempted to start using MC as my primary option-valuating technique as I can get ...
5
votes
2answers
521 views
VIX = Vega of S&P500 options?
ok, so let assume I can predict the daily change in the VIX itself (in points) every day. what would be the best way to play this with OPTIONS? well, obviously VIX options, but if I can look at the ...
1
vote
1answer
208 views
Portfolio Greek Exposure Equations
What are the calculations for calculating greek exposures in a portfolio of equities and equity options? I think I have them but I want to be sure. Are these correct (for vanilla options)?
...
15
votes
6answers
5k views
What are some useful approximations to the Black-Scholes formula?
Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$.
I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate ...
1
vote
2answers
327 views
Multi asset option portfolio risk management (greeks and FX exposure)
I am running an options book containing listed options across multiple products. I trade mostly equity and index related options - with a preference for European expiration products. I trade products ...
2
votes
1answer
145 views
Is there any evidence that an option delta approximates ITM expiry probability?
Several sources (online and offline) that discuss the delta of a listed vanilla option, state that its delta is a (guesstimate?) of the probability of said option expiring ITM (in the BSM framework).
...
1
vote
1answer
116 views
Brent Crude Data
I am trying to locate historical volatility data (5+ years) for Brent Crude? Does anyone know where I might be able to source such data?
2
votes
2answers
314 views
Why don't options traders use charts? Or do they?
Retail trading platforms typically offer equity charts but only instantaneous quotes on options. It seems like even a few minutes of historical data would be useful when entering an order. Are charts ...
2
votes
3answers
272 views
Basic question about Black Scholes derivation
In the derivation of the Black Scholes equation, the value of the portfolio at time $t$ is given by
$$P_t = -D_t + \frac{{\partial D_t}}{{\partial S_t}}S_t $$
where $P_t$ is the value of the ...
0
votes
1answer
166 views
Exotic option pricing
I'm trying to price an option with payoff $\max\{a\cdot S_t - K,0\}$ where $a$ is a known constant. Ideally I'm looking for a closed form, continuous-time solution. Where should I begin?
6
votes
1answer
173 views
Prove or disprove “If at least 10% of an option's value is time value, it has a delta less than 90”
"If at least 10% of an option's value is time value (ie. time value >= 0.1*call price), it has a delta less than 90".
In practice and after doing many tests with an option pricing calculator, this ...
6
votes
1answer
745 views
What is the best live options data API?
What is the best/cheapest service to get real-time (as real-time as you can get) on stock options?
I'm looking for the fastest update on the ENTIRE market, with a few stocks prioritized, so I need ...
5
votes
2answers
795 views
Implied Volatility from American options (binomial)
I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock).
I believe it is ...
3
votes
1answer
386 views
Science behind options pricing into Earnings event
I am wondering about studies regarding the uncanny options pricing into public company's earnings reports.
The phenomenon being that the price of a straddle before earnings costs near exactly the ...
2
votes
0answers
85 views
Option symbol conversion [closed]
Maybe more of a programming question,
Is there a Ruby gem to facilitate conversion of an option symbol notation from one form to another?
For example, one source provides TZA1220J18
but an API for ...
3
votes
0answers
110 views
Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative
Let $X_t$ be an american style financial derivative with random exercise time $T$
where $t$ and $T$ belongs to some finite set $A$.
Buying this derivative requires the buyer to pay $p_t$ up to time ...
3
votes
1answer
82 views
Do Bond Put Dates always fall on Coupon Dates (for non-zero coupon bonds). Calculation rules for Coupon Dates
This may not be the most appropriate SE site to ask this question, but I can't seem to find a better place to ask, so here goes:
Do Puttable Bonds' put dates always fall on Coupon Dates? When they ...
-1
votes
2answers
179 views
What is the Benefit of holding a short option?
i am new to corporate finance and ask myself why a investor is interested in being short on a Option? The only he can win is a premium but he can loose much more. I understand with being a short I can ...
1
vote
1answer
178 views
Calculate historical (ATM) option prices with public data
I just saw the question How to calculate the most realistic historical option prices with additional publicly available parameters and I am interested in the step before that.
How can I calculate ...
1
vote
3answers
1k views
Why do some people claim the delta of an ATM call option is 0.5?
I am looking for a mathematical proof in terms of differentiating the BS equation to calculate Delta and then prove it that ATM delta is equal to 0.5.
I have seen many books quoting delta of ATM call ...
2
votes
0answers
64 views
Any thoughts on how Warren Buffet's B of A warrants might be “marked-to-market” by either counterparty?
It's not too long since Berkshire Hathaway got its 10-year warrants in Bank of America alongside its \$5 billion purchase of preferred stock. At the time I saw some discussion about the value of ...
9
votes
5answers
2k views
What is the implied volatility skew?
I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that a clear standard definition is not unanimously in place among practitioners.
So here is ...
10
votes
5answers
445 views
Is it ever possible that---because of illiquidity---exercising an out-of-the-money option is better than directly buying the stock?
Is there a case, where due to illiquidity, exercising out-of-the-money options could be better than directly buying the stock?
When a stock is too illiquid, there are some costs because of this ...
2
votes
0answers
90 views
How to find the upper bound of a digital option given some market data?
Given the price of a call equals to 5 with Strike 100, please find the upper bound (sup) of the digital option with strike 105.
I am not sure about the solution, but I write the condition like this,
...
5
votes
1answer
273 views
What are VIX back-month futures based on?
The VIX calculation is a weighted average of prices for front-month out-the-money options on the S&P index.
So for VIX futures, this makes sense for the front month vix futures (being based on a ...
7
votes
1answer
220 views
When pricing options, what precision should I work with?
I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
3
votes
1answer
341 views
Can American options with no dividends and zero risk-free rate be treated as European?
Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
2
votes
0answers
107 views
What is the highest frequency greek for options on futures on bonds?
I'm considering exchange traded options of futures on bonds. Options on bond futures are usually American, thus the Black model is out of question. Which is the most imporatant Greek with respect to ...
4
votes
2answers
337 views
Does put-call parity hold for a compound option with underlying American option?
Say there is an American put option that expires $N$ months from today.
A call-on-put (CoP) option provides the owner the right to buy the American put option in exactly $M < N$ months (but no ...
5
votes
2answers
581 views
Constructing an approximation of the S&P 500 volatility smile with publicly available data
Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW.
Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
7
votes
2answers
646 views
How to calculate the most realistic historical option prices with additional publicly available parameters
This is a follow up question of this one.
My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes.
The ...
3
votes
0answers
129 views
How companies choose earnings release dates, & effect on Implied Volatility
A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
