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1 answer
94 views

What is the P&L

I have a question about the P&L calculation, please. If we sell a call option on a stock with a volatility of 16%. Theta is worth 100€/day. Let's assume that the spot moves by 2% in one day. What ...
2 votes
4 answers
327 views

How to short an option?

It appears to me that retail investors can only buy calls and puts, but not short them through any standardized way (except maybe borrowing the option from a friend ;) ). Is that correct, or how can ...
0 votes
1 answer
46 views

Obtain B-S-M from a binomial tree as n goes to infinty using Lebesgue integral

My question is simple, consider a European call with payoff max(S_T-K, 0), Let's suppose that the underlying stock follows a binomial tree with up and down factors I know as we take n goes to infinity ...
1 vote
3 answers
181 views

Why do one's current holdings matter when selling calls?

I was reading about selling calls, where there is a distinction between selling a naked call versus a covered call. I fail to understand why owning the underlying matters in the case the call's buyer ...
1 vote
0 answers
128 views

Heston model characteristic function

The characteristic function of $x=ln(S_T)$ in the framework of Heston model is guessed to be: $$f_j(\phi,x,v)=e^{C_j(\tau,\phi)+D_j(\tau,\phi)+i\phi x}$$ The call price is guessed to have the form: $$...
0 votes
0 answers
46 views

The call price can be above the underlying asset's current price ? And why call et put price are approximated by the same formula? [duplicate]

i have two questions which are simple i think. Is it possible for a call option to be issued on the market with a strike price higher than the underlying asset's current price? In a market without ...
0 votes
1 answer
233 views

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 ...
4 votes
5 answers
10k views

Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
1 vote
1 answer
67 views

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 ...
1 vote
1 answer
51 views

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 $\alpha_1$ ...
16 votes
5 answers
48k views

Bachelier model call option pricing formula

Does anybody have the Bachelier model call option pricing formula for $r > 0$? All the references I've read assume $r = 0$. I don't speak French, so I can't read Bachelier's original paper.
-1 votes
1 answer
280 views

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_{...
3 votes
1 answer
604 views

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 ...
2 votes
0 answers
99 views

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(...
1 vote
0 answers
261 views

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 : ...
0 votes
1 answer
190 views

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 ...
3 votes
1 answer
238 views

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 $f$ ...
3 votes
1 answer
451 views

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&...
1 vote
0 answers
92 views

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 ...
2 votes
1 answer
345 views

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 ...
0 votes
0 answers
76 views

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) ...
1 vote
0 answers
107 views

local volatility not reasonable

We are going to generate synthetic option prices using a Heston model, i.e., $$ \begin{gather*} dS_t = \sqrt{v_t} S_t dZ_t,\\ dv_t = \lambda (\mu - v_t) d_t + \eta \sqrt{v_t} dW_t, \end{gather*} $$ ...
0 votes
1 answer
98 views

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 ...
2 votes
1 answer
277 views

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 ...
1 vote
0 answers
148 views

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 ...
0 votes
1 answer
605 views

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/...
2 votes
1 answer
486 views

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 ...
0 votes
1 answer
134 views

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 ...
9 votes
4 answers
24k views

What does it mean to be "long or short in volatility"?

I've heard a question regarding pricing of european calls. The question is: Is the call long or short in volatility when it is (deep) OTM? What is the profile of the implied volatility? I know ...
1 vote
1 answer
314 views

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 ...
0 votes
1 answer
87 views

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 ...
1 vote
0 answers
516 views

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 ...
-2 votes
1 answer
94 views

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 ...
3 votes
1 answer
231 views

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 ...
0 votes
0 answers
81 views

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): ...
0 votes
0 answers
164 views

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 ...
1 vote
1 answer
391 views

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 ...
0 votes
1 answer
55 views

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 ...
0 votes
0 answers
43 views

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 ...
0 votes
1 answer
52 views

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. ...
2 votes
1 answer
1k views

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}{...
0 votes
0 answers
49 views

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
7 votes
3 answers
2k views

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 ...
1 vote
2 answers
174 views

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 ...
5 votes
1 answer
250 views

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,...
1 vote
1 answer
68 views

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 ...
2 votes
1 answer
285 views

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 ...
0 votes
0 answers
115 views

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. ...
1 vote
0 answers
104 views

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 ...
-1 votes
1 answer
270 views

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 ...