{"id":14577,"date":"2022-10-08T09:12:57","date_gmt":"2022-10-08T03:42:57","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-what-is-wrong-with-this-binomial-tree-backwards-induction-european-call-option-pricing-function\/"},"modified":"2022-10-08T09:12:57","modified_gmt":"2022-10-08T03:42:57","slug":"solved-what-is-wrong-with-this-binomial-tree-backwards-induction-european-call-option-pricing-function","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-what-is-wrong-with-this-binomial-tree-backwards-induction-european-call-option-pricing-function\/","title":{"rendered":"[Solved] What is wrong with this Binomial Tree Backwards Induction European Call Option Pricing Function?"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-64298637\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"64298637\" data-parentid=\"64144956\" data-score=\"0\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>I am note sure if you can omit that loop in an efficient way, but when we do not use <code>np.delete()<\/code> but just use the indices to shrink <code>payoff<\/code> in every iteration I already got a big speed increase on my machine:<\/p>\n<pre class=\"lang-py prettyprint-override\"><code># ...\narr = np.full(N+1, d\/u)\narr[0] = S*np.power(u, N)\narr[1:] = arr[0] * np.cumprod(arr[1:])\n\ndef get_payoff(s, k):\n    return np.maximum((s - k), 0)\n\npayoff = get_payoff(arr, K)\n\ndef binomial_tree(payoff,S,K,T,r,sigma,N):\n    for i in range(0, N):\n        payoff = coeff*(p*payoff[:-1] + (1-p)*payoff[1:])\n    return payoff[0]\n<\/code><\/pre>\n<p>Note that I also changed the generation of <code>arr<\/code> to be without a loop and changed the name of the <code>payload()<\/code> function so that it does not interfere with the variable name.<\/p>\n<hr>\n<h1>EDIT<\/h1>\n<p>I asked a similar question because I thought your formula was interesting and the answer from Frank Yellin also applies here (so all credits to him):<\/p>\n<pre class=\"lang-py prettyprint-override\"><code>import numpy as np\nfrom scipy.stats import binom\n\nbinomial = binom(p=p, n=N)\npmf = binomial(np.arange(N+1))\nres = coeff**n*np.sum(payoff * pmf)\n<\/code><\/pre>\n<p>In this form it is also clearer what is calculated in your loop:<br \/>\nthe expected value of the binomial distributed random variable payoff.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">0<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved What is wrong with this Binomial Tree Backwards Induction European Call Option Pricing Function? <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] I am note sure if you can omit that loop in an efficient way, but when we do not use np.delete() but just use the indices to shrink payoff in every iteration I already got a big speed increase on my machine: # &#8230; arr = np.full(N+1, d\/u) arr[0] = S*np.power(u, N) arr[1:] = &#8230; <a title=\"[Solved] What is wrong with this Binomial Tree Backwards Induction European Call Option Pricing Function?\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-what-is-wrong-with-this-binomial-tree-backwards-induction-european-call-option-pricing-function\/\" aria-label=\"More on [Solved] What is wrong with this Binomial Tree Backwards Induction European Call Option Pricing Function?\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[581,349],"class_list":["post-14577","post","type-post","status-publish","format-standard","hentry","category-solved","tag-numpy","tag-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] What is wrong with this Binomial Tree Backwards Induction European Call Option Pricing Function? 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