# Tagged Questions

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.

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### 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 ...
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### 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 ...
3k 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 ...
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### 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 ...
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### 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 no-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
1k views

### Why the interest rate for put-call parity is not constant?

Usimg the put-call parity $C - P = S - K · e^{-rt}$ I tried to estimate the value of $e^{-rt}$, the present value of a zero-coupon bond that matures to 1 in time $t$: $e^{-rt} = (P - C + S) / K$ ...
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### Pair Trading Index Options

Suppose the trade is between Index Options of two Indices X and Y which are quite similar (but not exactly). So for the equivalent strikes, one can quote option on Index X and cover in Index Y. But ...
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### 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 ...
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### 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)? ...
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### 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 ...
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### 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 ...
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### 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). ...
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### 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?
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### 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 ...
368 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 ...
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### 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?
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### 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 ...
748 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 ...
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### 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 ...
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### 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 $T$...
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### 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 ...
3k views

### What really drives option implied volatility?

A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
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### 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 ...
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### 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 ...
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### 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, ...
1k 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 ...
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### Eurodollar Options Stike Price > 100 bps

Looking at Eurodollar IR options market data coming down from CME, I can see a whole host of options where the strike is > 100 bps. My understanding in this case is that puts will always be in the ...