How to compute the dynamic of stock using Geometric Brownian Motion?A question on ItoGeometric Brownian...

Boss asked me to sign a resignation paper without a date on it along with my new contract

Is Screenshot Time-tracking Common?

SQL Server Service does not start automatically after system restart

How do I purchase a drop bar bike that will be converted to flat bar?

Including proofs of known theorems in master's thesis

Identical projects by students at two different colleges: still plagiarism?

Do the speed limit reductions due to pollution also apply to electric cars in France?

Why write a book when there's a movie in my head?

What is the Buddhist view in Socratic questioning?

Missing a connection and don't have money to book next flight

Sets which are both Sum-free and Product-free.

Is there any danger of my neighbor having my wife's signature?

C++ range based loop with special case for first item?

How can I differentiate duration vs starting time

What does "don't have a baby" imply or mean in this sentence?

Is it possible to narrate a novel in a faux-historical style without alienating the reader?

Are one-line email responses considered disrespectful?

What is the reward?

Protagonist constantly has to have long words explained to her. Will this get tedious?

How can I handle players killing my NPC outside of combat?

Did ancient Germans take pride in leaving the land untouched?

Is there a way to pause a running process on Linux systems and resume later?

How do I fight with Heavy Armor as a Wizard with Tenser's Transformation?

How do I avoid the "chosen hero" feeling?



How to compute the dynamic of stock using Geometric Brownian Motion?


A question on ItoGeometric Brownian motion - Volatility Interpretation (in the drift term)How to get Geometric Brownian Motion's closed-form solution in Black-Scholes model?Square of arithmetic brownian motion processSimulate drifted geometric brownian motion under new measureIto's Lemma, differentiating an integral with Brownian motionGiven $S$ is a Geometric Brownian Motion, how to show that $S^n$ is also a Geometric Brownian Motion?Stochastic process and brownian motionNormalized Gains Process is a Q-Martingale - Proof and IntuitionHow to derive the dynamic of the log forward price?













2












$begingroup$


I have been given the following question:




Given that $S_t$ follows Geometric Brownian Motion, write down the dynamic of $S_t$ and then compute the dynamic of $f(t,S_t) = e^{tS^{2}}$




For the first part of the question, I have got this answer:
$$dS_t = mu S_tdt + sigma S_t dWt$$



Is it correct?



And for the second part, I know that the price $f(t,S_t)$ follows the process
$$df = (frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2} sigma ^2S_tfrac{partial^2f}{partial S_t^2})dt +sigma S_t dWt$$



I am having trouble finding the answer using this process and given the information.



Any help is appreciated.






black-scholes stochastic-processes stochastic-calculus







share|improve this question











$endgroup$

















    2












    $begingroup$


    I have been given the following question:




    Given that $S_t$ follows Geometric Brownian Motion, write down the dynamic of $S_t$ and then compute the dynamic of $f(t,S_t) = e^{tS^{2}}$




    For the first part of the question, I have got this answer:
    $$dS_t = mu S_tdt + sigma S_t dWt$$



    Is it correct?



    And for the second part, I know that the price $f(t,S_t)$ follows the process
    $$df = (frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2} sigma ^2S_tfrac{partial^2f}{partial S_t^2})dt +sigma S_t dWt$$



    I am having trouble finding the answer using this process and given the information.



    Any help is appreciated.






    black-scholes stochastic-processes stochastic-calculus







    share|improve this question











    $endgroup$















      2












      2








      2





      $begingroup$


      I have been given the following question:




      Given that $S_t$ follows Geometric Brownian Motion, write down the dynamic of $S_t$ and then compute the dynamic of $f(t,S_t) = e^{tS^{2}}$




      For the first part of the question, I have got this answer:
      $$dS_t = mu S_tdt + sigma S_t dWt$$



      Is it correct?



      And for the second part, I know that the price $f(t,S_t)$ follows the process
      $$df = (frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2} sigma ^2S_tfrac{partial^2f}{partial S_t^2})dt +sigma S_t dWt$$



      I am having trouble finding the answer using this process and given the information.



      Any help is appreciated.






      black-scholes stochastic-processes stochastic-calculus







      share|improve this question











      $endgroup$




      I have been given the following question:




      Given that $S_t$ follows Geometric Brownian Motion, write down the dynamic of $S_t$ and then compute the dynamic of $f(t,S_t) = e^{tS^{2}}$




      For the first part of the question, I have got this answer:
      $$dS_t = mu S_tdt + sigma S_t dWt$$



      Is it correct?



      And for the second part, I know that the price $f(t,S_t)$ follows the process
      $$df = (frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2} sigma ^2S_tfrac{partial^2f}{partial S_t^2})dt +sigma S_t dWt$$



      I am having trouble finding the answer using this process and given the information.



      Any help is appreciated.






      black-scholes stochastic-processes stochastic-calculus




      black-scholes stochastic-processes stochastic-calculus






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 3 hours ago









      Emma

      27112




      27112










      asked 3 hours ago









      Rito LoweRito Lowe

      164




      164






















          1 Answer
          1






          active

          oldest

          votes


















          3












          $begingroup$

          The above equation should correctly read as follows:



          $df=big(frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2}sigma^2 S_t^2frac{partial^2 f}{partial S_t^2}big)+sigma S_t frac{partial f}{partial S_t}dW$



          Using:



          (a) $frac{partial f}{partial t}=S_t^2f$



          (b) $frac{partial f}{partial S_t}=2S_ttf$



          (c) $frac{partial^2 f}{partial S_t^2}=2tf+4S_t^2t^2f$



          The Stochastic Differential Equation (SDF) governing the dynamics of $f$ becomes:



          $frac{df}{f}=dt big(S_t^2+2 mu S_t^2t+sigma^2S_t^2t+2sigma^2S_t^4t^2 big)+2S_t^2tsigma dW$






          share|improve this answer











          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "204"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f44220%2fhow-to-compute-the-dynamic-of-stock-using-geometric-brownian-motion%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            3












            $begingroup$

            The above equation should correctly read as follows:



            $df=big(frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2}sigma^2 S_t^2frac{partial^2 f}{partial S_t^2}big)+sigma S_t frac{partial f}{partial S_t}dW$



            Using:



            (a) $frac{partial f}{partial t}=S_t^2f$



            (b) $frac{partial f}{partial S_t}=2S_ttf$



            (c) $frac{partial^2 f}{partial S_t^2}=2tf+4S_t^2t^2f$



            The Stochastic Differential Equation (SDF) governing the dynamics of $f$ becomes:



            $frac{df}{f}=dt big(S_t^2+2 mu S_t^2t+sigma^2S_t^2t+2sigma^2S_t^4t^2 big)+2S_t^2tsigma dW$






            share|improve this answer











            $endgroup$


















              3












              $begingroup$

              The above equation should correctly read as follows:



              $df=big(frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2}sigma^2 S_t^2frac{partial^2 f}{partial S_t^2}big)+sigma S_t frac{partial f}{partial S_t}dW$



              Using:



              (a) $frac{partial f}{partial t}=S_t^2f$



              (b) $frac{partial f}{partial S_t}=2S_ttf$



              (c) $frac{partial^2 f}{partial S_t^2}=2tf+4S_t^2t^2f$



              The Stochastic Differential Equation (SDF) governing the dynamics of $f$ becomes:



              $frac{df}{f}=dt big(S_t^2+2 mu S_t^2t+sigma^2S_t^2t+2sigma^2S_t^4t^2 big)+2S_t^2tsigma dW$






              share|improve this answer











              $endgroup$
















                3












                3








                3





                $begingroup$

                The above equation should correctly read as follows:



                $df=big(frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2}sigma^2 S_t^2frac{partial^2 f}{partial S_t^2}big)+sigma S_t frac{partial f}{partial S_t}dW$



                Using:



                (a) $frac{partial f}{partial t}=S_t^2f$



                (b) $frac{partial f}{partial S_t}=2S_ttf$



                (c) $frac{partial^2 f}{partial S_t^2}=2tf+4S_t^2t^2f$



                The Stochastic Differential Equation (SDF) governing the dynamics of $f$ becomes:



                $frac{df}{f}=dt big(S_t^2+2 mu S_t^2t+sigma^2S_t^2t+2sigma^2S_t^4t^2 big)+2S_t^2tsigma dW$






                share|improve this answer











                $endgroup$



                The above equation should correctly read as follows:



                $df=big(frac{partial f}{partial t}+mu S_t frac{partial f}{partial S_t}+frac{1}{2}sigma^2 S_t^2frac{partial^2 f}{partial S_t^2}big)+sigma S_t frac{partial f}{partial S_t}dW$



                Using:



                (a) $frac{partial f}{partial t}=S_t^2f$



                (b) $frac{partial f}{partial S_t}=2S_ttf$



                (c) $frac{partial^2 f}{partial S_t^2}=2tf+4S_t^2t^2f$



                The Stochastic Differential Equation (SDF) governing the dynamics of $f$ becomes:



                $frac{df}{f}=dt big(S_t^2+2 mu S_t^2t+sigma^2S_t^2t+2sigma^2S_t^4t^2 big)+2S_t^2tsigma dW$







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 1 hour ago









                Emma

                27112




                27112










                answered 2 hours ago









                ZRHZRH

                583112




                583112






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Quantitative Finance Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f44220%2fhow-to-compute-the-dynamic-of-stock-using-geometric-brownian-motion%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    Szabolcs (Ungheria) Altri progetti | Menu di navigazione48°10′14.56″N 21°29′33.14″E /...

                    Image
                    Comuni della provincia di Szabolcs-Szatmár-Bereg Ungheria2001provincia di Szabolcs-Szatmár-Bereg Szabolcs comune Localizzazione Stato   Ungheria Regione Grande Pianura Settentrionale Provincia Szabolcs-Szatmár-Bereg Territorio Coordinate 48°10′14.56″N 21°29′33.14″E  /  48.17071°N 21.49254°E 48.17071; 21.49254  ( Szabolcs ) Coordinate: 48°10′14.56″N 21°29′33.14″E  /  48.17071°N 21.49254°E 48.17071; 21.49254  ( Szabolcs ) Superficie 5,88 km² Abitanti 425 (2001) Densità 72,28 ab./km² Altre informazioni Cod. postale 4467 Prefisso 42 Fuso orario UTC+1 Codice KSH 19169 Cartografia Szabolcs Sito istituzionale Modifica dati su Wikidata  · Manuale Szabolcs è un comune dell'Ungheria di 425 abitanti (dati 2001). È situato nella provincia di Szabolcs-Szatmár-Bereg. Altri progetti | Altri progetti Wikimedia Commons Wikimedia Commons contiene immagini o altri file su Szabolcs .mw-parser-output
                    Read more

                    Discografia di Klaus Schulze Indice Album in studio | Album dal vivo | Singoli | Antologie | Colonne...

                    Image
                    Discografie di artisti tedeschi Voce principale: Klaus Schulze . Discografia di Klaus Schulze Klaus Schulze e Lisa Gerrard durante un concerto Album in studio 56 ↙ Album dal vivo 15 ↙ Raccolte 37 ↙ Singoli 4 ↙ Album video 1 ↙ Colonne sonore 4 ↙ Indice 1 Album in studio 1.1 Solisti 1.1.1 Come Richard Wahnfried 1.2 Collaborazioni 1.2.1 Con Rainer Bloss 1.2.2 Con Rainer Bloss ed Ernst Fuchs 1.2.3 Con Lisa Gerrard 1.2.4 Con Andreas Grosser 1.2.5 Con Pete Namlook 1.2.6 Con Pete Namlook e Bill Laswell 1.2.7 Con Michael Shrieve 1.2.8 Con Solar Moon 1.2.9 Con artisti vari 2 Album dal vivo 3 Singoli 4 Antologie 5 Colonne sonore 6 Videografia 7 Collegamenti musica Album in studio | Solisti | 1972 – Irrlicht 1973 – Cyborg 1974 – Blackdance 1975 – Timewind 1975 – Picture Music 1976 – Moondawn 1977 – Mirage 1978 – "X" 1979 – Dune
                    Read more

                    How to make inet_server_addr() return localhost in spite of ::1/128RETURN NEXT in Postgres FunctionConnect to...

                    Image
                    Potential client has a problematic employee I can't work with Can the "Friends" spell be used without making the target hostile? Does it take energy to move something in a circle? Why are carbons of Inositol chiral centers? Count repetitions of an array Which RAF squadrons and aircraft types took part in the bombing of Berlin on the 25th of August 1940? Memory usage: #define vs. static const for uint8_t Broad Strokes - missing letter riddle Why does 0.-5 evaluate to -5? Why is 'diphthong' pronounced the way it is? Why did Luke use his left hand to shoot?
                    Read more