Questions tagged [call]
The call tag has no usage guidance.
119
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Is there economic/intuitive reason why the treynor-black model favour low delta instruments?
In the treynor-black model optimal instrument weights are proportional to:
$w_i = \frac{\frac{\alpha_i}{\sigma_i^2}}{\sum_j \frac{\alpha_j}{\sigma_j^2} }$.
Let Instrument 1 be a stock with $\alpha_1$ ...
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Call Value After 98 percentile drop in Stock Price
This question is from Joshi's quant book.
Assume r = 0, σ = 0.1, T-t = 1, X = 100 = S(t).
Initially, the call is worth $3.99.
The first question asks what the value of the call is after a 98 ...
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Call option on forward [closed]
What is the trade description behind a call option on a forward? How can it be described with words and not with mathematical formulas?
So what is the intuition behind the following payoff:
$$Payoff_{...
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0
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Path integral approach to price call option on zero coupon bonds
I am given the following identities:
$$
Z[J,t_1,t_2]=\int D W e^{\int_{t_1}^{t_2}dtJ(t)W(t)}e^{S}=e^{\frac{1}{2}\int_{t_1}^{t_2}dtJ(t)^2}
$$
$$
\int_t^Tdx\alpha(t,x)=\frac{1}{2}\left[\int_t^Tdx\sigma(...
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Call probability of a callable swap
For one call date,
The call probability is just the probability that the swap rate for the remaining life of the swap is below the strike rate. This is easily obtainable in a normal vol model, it is :
...
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Given $\mathbb{E}[X]$, $\mathbb{E}[\max(0,X)]$, and $\mathbb{E}[\min(0,X)]$, what is $\mathbb{E}[f(X)]$
Let $X$ be any random variable with any distribution. Given that we know $\mathbb{E}[X]$, $\mathbb{E}[\max(0,X)]$, and $\mathbb{E}[\min(0,X)]$, can you write a formula for $\mathbb{E}[f(X)]$ where $f$ ...
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Can we trade theta?
The context is this theoretical result from Black-Scholes-Merton differential equation that the effects of theta and gamma cancel each other.
Equation (5.23) from the book titled "Option Trading&...
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0
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Why IV surface over call price surface? [closed]
Why do options traders usually model and trade the IV surface? I appreciate that the IV surface is more standard across assets, but why do we go to so much trouble with the IV surface?
To me it seems ...
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Why is this inequality strict for arbitrage argument for European call?
in the notes about arbitrage arguments I am reading, I notice the statement
We can also see that
$$C^E_t>(S_t-K\mathrm{e}^{-r(T-t)})^+$$
Notice that the inequality holds STRICTLY!
I don't ...
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Can the Feynman-Kac formula be used for asset classes that don’t have options?
So rather than a call option C(S_t,t) we have some type of asset with asset price is given by S(x,t) where x is any type of variable that the asset price depends on. I.e Price of wooden desks, W(x,t) ...
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local volatility not reasonable
We are going to generate synthetic option prices using a Heston model, i.e.,
$$
\begin{gather*}
dS_t = \sqrt{v_t} S_t dZ_t,\\
dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t,
\end{gather*}
$$
...
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Pricing for basic option strategies [closed]
If I am trying to price a strategy, say for example a call spread where we are long a call, strike L and short a call strike M, would the pricing formula simply be the Black-Sholes price for the Call ...
1
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1
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247
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Greeks of portfolio in response to underlying price change
I'm trying to wrap my head around Greeks, and I'm getting a little bit confused. For example, let's say my portfolio holds a long 5 month ATM call with strike \$20, and short 2 month OTM call with ...
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Replicating call option in market which only trades stock and forward contracts
I am having a bit of trouble with a problem I've been given.
Consider a market which only trades a stock and forward contracts. There's only time 0 and 1.
Initial stock price S_0 is 10, the forward ...
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420
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Callable Corporate Bonds: Why Issue a Callable Bond That Has a First Call Date <6 months to Final Maturity?
My understanding is that firms typically issue callable bonds to benefit from possible refinancing in a lower interest rate environment. What, then, is the point of issuing a bond, say, today (06/30/...
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408
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Gamma-neutral delta-neutral call ratio spread
I have been looking into options strategies that minimize risk via delta neutrality. One such strategy seems to be the gamma-neutral delta-neutral call ratio spread, in which the gamma is neutralized ...
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How are the greeks defined for the two legs or more strategies with regards to options?
I am to figure out something, and can't find any reference. I wonder: does it make sense to talk of a delta or other greek of a strategy? It seems that you can't put a price exactly on a call spread ...
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Maximum value of a call option proof [closed]
I'm reading Sinclair's Option Pricing and am confused by the proof for the maximum value of a call. It makes sense logically that a call can't be worth more than the underlying, and so:
c <= S
The ...
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Why does the price of an option increase with increasing Rho?
I was wondering why the price of an option increases with Rho (price change for a derivative relative to a change in the risk-free rate of interest).
I found this explanation on a website:
"Each ...
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Confused in regards to calculation of delta of one share including one call and one put [closed]
Q:My investment portfolio has one share of one call and one put, what would be the delta of my portfolio ?
delta of call:0.45
delta of put: -0.14
My thought process:
To begin with since im dealing ...
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1
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Derivation for call option upper bound
In Euan Sinclair's book, Option Trading, he writes that $c <= S$, the price of a European call must be lower than the price of the underlying stock. To prove it, he applies the principle of no ...
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Heston Model Calibration with MatLab: model prices do not fall in the bid-ask range
I am currently implementing the MatLab code reported below for the calibration of Heston Model. The code seems fine and, by reading the paper where I took the code, I was able to calibrate and price ...
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Pricing a European call option that has one underlying asset to compare with strike but 2 underlyings as payout
This is a real world problem and not a research one.
We are being proposed to buy an option that has to be exercised on a specific date T. So it is a European option.
This option has a strike price of ...
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3
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1
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218
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Digital call under Ornstein-Uhlenbeck dynamics
I am trying to price a digital option with payoff $\mathbb{I}_{S_T>K}$, where $S_t$ follows the Ornstein-Uhlenbeck dynamics $\mathrm{d}S_t=rS_t\mathrm{d}t+\sigma\mathrm{d}W^{\mathbb{Q}}_t$ in the ...
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What can we say about digital puts and calls with different strike prices?
I am a noob to the field of quantitative finance. I am reading this book by Mark S. Joshi. Can you help me make sense of one of the exercise questions? Here is the question (from page 40 of the book):
...
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Payoff of barrier options
I was reading a research paper recently and the author defined payoffs of Up-and-Out and Down-and-Out barrier call options as max[0, ST - K]I(m < H) and max[0, ST - K]I(M > H) respectively.
K is ...
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Call spread hedge
I'm trying to understand how a call spread is used for FX hedging. The example that my book gives is when we have USD receivables in 12 months which we want to convert to EUR and we want to hedge ...
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Why did Tiffany call's premium increase, when its stock price decreased? [closed]
My grandma has been tracking TIF in the news, and recorded its option premiums. On Jun 9 2020, 1 TIF 2022-01-22 135C sold for \$0.88. On Jun 10 2020, it sold for \$0.5. Today, it sold for $1.6. Which ...
user31928
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Deterministic optimal call time
Consider a American Option on a linear payoff i.e., if called at time $T$, it pays off $S(T)$, the stock price. Is the optimal call time of such an option determinsitc? Is there an intuition to the ...
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Can the spread between option premium for bull call spread change over time?
I have created a bull call spread. There was spread of 70 dollars between the option premium of 2 strikes I selected. Now the spread between option premium of 2 strikes is greater than 100 dollars. ...
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Black-Scholes Formula under $T$-forward measure
The Black-Scholes price of a European call option is given by
$$ C_0^{BS}(T, K) = \mathbb{E}_Q[e^{-rT}(S_T - K)_+] = S_0 \Phi(d_1) - Ke^{-rT}\Phi(d_2) ,$$
where
$$ d_{1,2} = \frac{\log\big(\frac{S_0}{...
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VaR of protfolio with put and call
I've stumbbled into this question in a job interview and didn't know how to answer it:
Calculate the VaR of a portfolio where you are long put and long a call
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Which is riskier: a call option or the underlying?
From Joshi's Quant Interview Questions and Answers:
What is riskier: a call option or the underlying? (Consider a one day time horizon and compute which has bigger Delta as a fraction of value).
I ...
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Failing to replicate Wilmott's results for binomial option pricing
I am working through Paul Wilmott introduces Quantitative Finance, 2nd ed. I am failing to reproduce one of his numerical examples and I would like to understand why.
I chapter 3, Wilmott introduces ...
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FX Call under stochastic rates and deterministic volatility
Lets denote $S_t$, $r^d_t$,$r^f_t$ respectively the FX spot, the domestic rate and the foreign rate at time $t$.
Lets $\mathbb{Q}^d$ , $\mathbb{Q}^f$ respectively be the domestic and foreign mesures,...
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call vs average of prices
Consider a two-period binomial model, with one risky asset. The are two types of options:
call option with strike price $K$, i.e., the payoff is given by $g(S_T)=(S_T-K)^{+}$
option with payoff given ...
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Geometric brownian motion and probabilities
A stock's price movement is described by the equations $dS_t=0.02S_tdt+0.25S_tdW_t$ and $S_0=100$. An investor buys a call option on said stock with a strike price $K=95$ which expires in $T=2$ years. ...
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Double Call Option
A double call option allows the holder to either exercise at time $T_{1}$ or time $T_{2}$, where $T_{2}$>$T_{1}$. With corresponding strike prices $K_{1}$ and $K_{2}$, it can be shown that it is never ...
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Call Probability of European callable IRS [closed]
When pricing a callable IRS (say only one call date) with a diffusion model (e.g. HW 1F) with a Montecarlo resolution, one can get the call probability on the call date versus maturing the date (which ...
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What is a call-spread and its formula?
I am attempting Mark Joshi's The Concepts and Practice of Mathematical Finance.
In B.3 Project 1: Vanilla options in a Black-Scholes world, he asked the following question.
We need to be sure that ...
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Cash-or-Nothing Call Option
I am trying to price a cash or nothing call option and I know know that the Cash or Nothing formula for a call option is $C(t,s)=Xe^{-r(T-t)}*N(d)$
If I have payoff X=100 r=0.03 T=2 $\sigma=0.3$
I ...
1
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2
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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}}$$
Is there an intuitive explanation for why this ...
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Graph of European call option value versus future price
Given a standard European call option on a non-dividend-paying stock. Draw the graph of call price at time $t$ versus the future price $F(t,T)$. The future price $F(t,T)$ is observed at time $t$, ...
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Boundaries for Call Spread
I'm reading an interview book called A Practical Guide to Quantitative Finance Interview and I have some doubts regarding part of its solution and highlighted them in bold:
Question:
What are the ...
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Is the vega of a portfolio of a long 0.5 delta and short two 0.25 delta calls positive or negative?
More specifically what I am trying to find out is whether the following relationship is always true or not. Same underlying for the calls, assume the most simplistic assumptions (interest rate = ...
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Why is higher the call price, the higher the price of a callable bond?
I am preparing for FRM level 2, but I ran into a question whose answer was confusing to me:
In the answer, it says "all other things remaining the same, the higher the call price, the higher the ...
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Binomial Model - completeness in presence of arbitrage
Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is
$$ V_0 = B_0 + hS_0, $$
...
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Risk Reversal quoting convention in FX market
How is RR bid offer quoted in market? For example: If a 25delta call and 25delta put is quoted as 5.5%/5.6% and 5.3%/5.5% respectively. What would be quote of a 25d RR with these call and Put?
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European Call option replication
An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time.
I use a Monte Carlo algorithm to ...
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Calculate the price at time t=0
Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model
(with interest rate r, stock drift $\mu$ and volatility $\sigma$).
Calculate the price at time $t = ...
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