{"abstracts":[{"sha1":"a12edd2d30977faabbdbb08796f97494848b4d65","content":"We propose a new framework for modeling stochastic local volatility, with\npotential applications to modeling derivatives on interest rates, commodities,\ncredit, equity, FX etc., as well as hybrid derivatives. Our model extends the\nlinearity-generating unspanned volatility term structure model by Carr et al.\n(2011) by adding a local volatility layer to it. We outline efficient numerical\nschemes for pricing derivatives in this framework for a particular four-factor\nspecification (two \"curve\" factors plus two \"volatility\" factors). We show that\nthe dynamics of such a system can be approximated by a Markov chain on a\ntwo-dimensional space (Z_t,Y_t), where coordinates Z_t and Y_t are given by\ndirect (Kroneker) products of values of pairs of curve and volatility factors,\nrespectively. The resulting Markov chain dynamics on such partly \"folded\" state\nspace enables fast pricing by the standard backward induction. Using a\nnonparametric specification of the Markov chain generator, one can accurately\nmatch arbitrary sets of vanilla option quotes with different strikes and\nmaturities. Furthermore, we consider an alternative formulation of the model in\nterms of an implied time change process. The latter is specified\nnonparametrically, again enabling accurate calibration to arbitrary sets of\nvanilla option quotes.","mimetype":"text/plain","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Igor Halperin","role":"author"},{"index":1,"raw_name":"Andrey Itkin","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v2","ext_ids":{"arxiv":"1301.4442v2"},"release_year":2013,"release_date":"2013-03-27","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["7z6bjn6ibvgzbeypnlqcy6phwu"],"mimetype":"application/pdf","urls":[{"url":"https://archive.org/download/arxiv-1301.4442/1301.4442.pdf","rel":"archive"}],"sha256":"6a3ef8e9605e63be1d2b63e60a26c5744fbedddfbbac4d451d23db72fb5a0f72","sha1":"86ca83726d9ee782c301d4f35416b7a9f0bd9200","md5":"04b882d4b37f51e42c930b848299821e","size":1542107,"revision":"ea0f2519-6527-4904-80e9-d532fc3b3e57","ident":"snxbqjnvfncvfezvit5bwggsha","state":"active"}],"work_id":"awxtois7e5guja3k255dqrepme","title":"USLV: Unspanned Stochastic Local Volatility Model","state":"active","ident":"7z6bjn6ibvgzbeypnlqcy6phwu","revision":"ecf3f1aa-ec1c-4af4-a743-27f2d39e7763","extra":{"arxiv":{"base_id":"1301.4442","categories":["q-fin.PR","q-fin.CP"],"comments":"Sections 3.2 and 3.3 are re-written, 3 figures added"}}}