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.

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36 views

How many seconds of Longstaff Schwartz would it take to get machine accuracy?

Roughly speaking, using a standard programming language, a standard computer, and a standard implementation, how many seconds would it take to price an American put option to 10+ digits of accuracy in ...
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31 views

GARCH(1,1) estimation in R via fmincon

I try to replicate Duan's (1995) results on option pricing in GARCH model. I have the same dataset and I follow MLE method described in book Pricing Option under Stochastic Volatility (Pretoria 2003). ...
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Vol surface fitting with 5 degrees of freedom

For an options market making operation I need to be able to build a volatility surface, based on only 5 degrees of freedom, like e.g.: MaxPut, MaxCall, Skew, Curve and At The Money Vol. Is there an ...
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How to price a put option on a multi-asset fund? Confused by risk-neutral pricing implicaton on real world

The fund has super track record with stable vol. The chance for this Put to pay out is very low in real world, but a B/S risk-neutral pricing would give a very high cost. I am struggling with the ...
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113 views

Option pricing without analytical solutions

I am quite new to the topic of financial options. I'm aware of options with analytical solutions (e.g. European options in Black-Scholes and Ornstein-Uhlenbeck models). I read that sometimes (most ...
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Is a warrant with the same strike price and maturity as the corresponding call option priced in the same way as the call option?

Is a warrant with the same strike price and maturity as the corresponding call option priced in the same way as the call option? Suppose I find a strike X warrant with T years to expiry and a call ...
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79 views

Implied volatility for puts vs calls [duplicate]

I was trying to create a replication portfolio of options for a Variance Swap and noticed that there is a jump when moving from below strike puts to above strike calls. Something similar to this: I ...
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71 views

Short-Term Option Contract Worth Same as Long Term Option Contract At Same Strike?

Let's say that I'm analyzing option contracts for ABC Company, which typically trades at lower volumes. While researching ABC Company, I notice that for a given strike price, contracts that expire in ...
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understanding Greeks Hedging? [closed]

I know what the greeks (delta, gamma, thetha, etc.) mean in options, but could someone clearly explain how can someone hedge them? I hear delta hedging a lot, but it is difficult to put it on the ...
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35 views

Selecting strike prices for put-writing strategy based on Z-scores

I'm trying to replicate the put-writing strategy of Jurek and Stafford from 2015 (The Cost of Capital for Alternative Investments, Jrl. Fin. SSRN). Their strategy writes index put options on the SP500,...
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50 views

How to compute a portfolio value?

I am learning fundamentals of option market and ran into an example I do not understand : Let's assume I have a portfolio of 3 shares priced \$22, and a European call option to buy a share for \$21 ...
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98 views

On which model is based the Finite Differences method for implied volatility computations?

I am very new to finance, so I don't know if my question makes sense but I have seen that there are different methods to estimate the implied volatility of an American Option. One of them is the ...
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66 views

How to calculate the prices of option instruments for a new underlying

Can someone with practical experience with implementing and verifying please point me in the right direction. Let's say I have 3 months of data for an underlying. I want to generate theoretical ...
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68 views

Delta heding & PnL

Sorry if it's a duplicate but i didn't find an answer to my simple question in the other posts. Let say we short a call option on a stock. $K = 100$, $C = 1$, $S = 100$ and $\Delta = 0.5$. No ...
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138 views

Value at Risk for portfolio with different maturities

I am new to StackExchange and relatively new to quantitative finance. I work at a commodity trading company and we have an extensive portfolio of futures and options on commodities (traded on the CME, ...
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85 views

Zero Volatility Options Pricing

Suppose an asset evolves in time according to the SDE $$ dS = \mu S dt + \sigma S dW, $$ where $\mu>0,\sigma>0$ are fixed constants and $dW$ is a Wiener process. To price options for this ...
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38 views

Reputable source for historical US-listed EOD options data for backtesting

I've gone through the data thread and found a few viable options. ivolatility.com in particular has what I'm looking for (EOD US-listed NBBO options price data, volume, OI, history back to 2000) but ...
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Practical approach to get average option IV

Is there a practical method to calculate some sort of average IV for each level of moneyness of equity options? I'm thinking of an algorithm to find mispriced options and do to so, we need to figure ...
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66 views

Option on a dice game with three dices and min. value

We have a call option on 3 dices with strike 3. What's the fair value of the call when it pays the min value of the 3 dices? E.g if we throw and have 426, the min is 2 here and so call is OTM (S < ...
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112 views

Calculate forward price based on option chain

I've got historical data for a spy option chain which looks as follows ...
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1answer
54 views

Call options or put options with put-call parity

When pricing European call options, is it preferred to price them directly or pricing a put first, then using put-call parity? I've read somewhere that the latter method is preferred in some ...
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59 views

Risk Neutral Density Curve for SPY Options looks very weird

I have created a risk neutral density curve using SPY weekly options and the RND package in R. I calculated the risk neutral density for the Feb07 options. The curve looks very weird when I look at ...
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76 views

What model to price interest rate option if we have views on trend of forward interest rate?

Apart from classical Black-Scholes model which assumes that forward interest rate is (log) normally distributed, what kind of pricing tools can we use as a buy side? We have good estimation on how ...
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Risk-neutral price of $H=e^{X_T^1+X_T^3}$

Let $B=(B_t^1,B_t^2,B_t^3)$ a $\mathbb R^3$-valued Brownian motion. Let $r_t$ (risk free rate) be bounded and deterministic. Let consider the DISCOUNTED market $$d\overline X_t^1=\frac52dt+2dB_t^1-...
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Where can I find data about Options for Europe (entire dataset)?

I need to get data about the entire dataset (i.e. all) of options for European countries. Where can I do that? For example, if I had to do it for US options, I would just use WRDS (to which I have ...
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97 views

To use daily volatility or annual volatility

From Joshi's Quant Interviews books: The statistics department from our tell you that the stock price has followed a mean reversion process for the last 10 years, with annual volatility 10% and ...
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53 views

Quantlib specify contract duration instead of dates

I use the following code in Python to price American put/call options. It's simple code since I'm new to using Quantlib. I would like to specify the contract duration (i.e. ...
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124 views

What's the point of having an accurate option pricing model?

Just curious what's the actual reason of having an accurate option pricing model? For e.g. an option pricing model fits the volatility surface incredibly well, then what? Do practitioners actually use ...
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72 views

Greeks, European puts

I'm trying to solve this question but i have a lot of problems with it. European puts with maturity 6 months are written on an asset with current price $S_0=150.$ The annual interest rate is $r=16\%$ ...
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1answer
77 views

Risk Neutral Pricing and the Drift

For risk neutral pricing, why do we want to compute expectation of a martingale? why is this so important? Why do we dislike the drift so much? Avoid math heavy answers please.
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2answers
76 views

Deltas on Barrier options vs Vanilla options

In "Heard on the Street" it states that $$\Delta_{\text{up and out call}} \leq \Delta_{\text{standard call}} \leq \Delta_{\text{down and out call}}$$ Is there an intuitive explanation for why this ...
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56 views

Formula for the discounted payoff of a digital option

In "Heard on the Street" it states that the expected discounted payoff of a digital option is $$H\exp^{-r(T-t)}N(d_2)$$ where $H$ is the payoff of the option, the exponential is the discounting. ...
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69 views

Adjusting your delta hedge when the stock crashes and were originally delta hedged

You are long a call option on a stock and you are delta hedged. The stock crashes in price. How do you adjust your delta, do you buy or sell stock? Could answers please be quantitative (i am getting ...
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101 views

Proof that adding some quantity of stocks in a portfolio of option does not change the portfolio Gamma

I would like to proof mathematically and intuitively that adding some quantity of underlying to a portfolio of option does not change the overall gamma. Can you help me?
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63 views

Calculating Delta of option portfolio using average of inputs

Trying to think through two options portfolio scenarios, which are highly similar. I'm wondering if you can take a portfolio of options, all written against the same underlying product, and use ...
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58 views

Calculate upper bound for put option prices?

I need to know historical option prices for backtesting. The problem is I don't have such historical data. Is there a way to calculate the upper bound for out of money (American) put option selling ...
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51 views

Approximate Asian option price under Heston Model

I am looking to see if there is a formula or a derivation at least of an approximation of an Asian (Average Price) option under the heston model of stochastic volatility. Please advise
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Construction of Butterfly Spread as sum of Call Options

I have rigorously stated my problem here. The task at hand is to express a butterfly spread [no transaction fees] as a sum of long and short call options. I have found the solution on Wikipedia: $$\...
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48 views

Differences in bull put spread option strategy

I am supposed to construct a profit and loss diagram for a bullish spread strategy: −1put($X_{1}$) + 1put($X_{2}$) and compare it to the profit and loss diagram for the strategy: −10put ($X_{1}$)+ ...
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What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
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266 views

Can strike prices of options be negative?

I am trying to understand the stochastic model of a financial market in one period by [Föllmer, Schied]. They introduce call and put options for the primary assets, which are non-negative. They do not ...
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Where could I get European non-dividend option data

I am pretty new to option pricing. I got a task asking me to price a stock option, which should be an European non-dividend option, and compare my price to its quote. I used to use TSLA data ...
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Mark Joshi uses forward price to price an option that pays $S_t^2-K$ if $S_t^2>K $ and zero otherwise? Why can we do that?

The following question is taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, Exercise $6.6$ Suppose a stock follows geometric Brownian motion in a Black-Scholes ...
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In Carr-Madans option pricing method, why do they use FFT?

In the famous fourier option pricing method by Carr-Madan, (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4044&rep=rep1&type=pdf), the crucial formula is They evaluate this by ...
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72 views

Show that $Ae^{rt}$ is a solution of the Black-Scholes equation. Why should this be so?

The following is taken from Mark Joshi's Concepts and Practice of Mathematical Finance, second edition, exercise $5.6$. Question: Show that $Ae^{rt}$ is a solution of the Black-Scholes equation. ...
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How important is it that numerical methods can price for various strikes simultaneously?

I am reading a paper which presents a numerical method to price call options. Call this Method 1. The method can also price several call-options for a range of strikes simultaneously if you want it to,...
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Option PnL Attribution

I am trying to compute the pnl of an option where for the both days option greeks delta, gamma, vega, theta and stock price and IV is given. I know the option pnl will be the sum of delta pnl+ gamma ...
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What is the difference between exercise and expiry date?

I know in American options you can exercise the options at any time before expiry date but in European options you can only exercise the options on expiry day. On National Stock Exchange of India the ...
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Confusion about bid- ask- and last-prices from option prices data

I’m struggling with the interpretation of quoted option prices I obtained from Bloomberg. The call options prices are available for a daily time series with different strikes at a given day. I ...
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Relationship between Calendar Spread Arbitrage and Probability Density Function (pdf)

We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $\partial ^2C/\partial K^2 \geq 0$, which also means the ...

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