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Abstract The valuation of equity swap under the condition of risk neutral is similar to the forward interest rate swap with the same period. Therefore, its valuation formula is consistent to interest rate swap model in the traditional methods. But it is not the same as in pricing the cross-currency equity swap. The dymanic prices of foreign stock index and exchange rate, and the correlation coefficients between exchange rates and foreign assets also affect the swap rate. In this paper, we extend Chance and Rich(1998)¡¦s valuation formula of equity swaps, and apply Amin (1991)¡BAmin and Bodurtha(1995)¡BLin(1997)¡¦s dymanic prices of assets in discrete time period. To derive the risk neutral valuation formula of equity swap, it uses the method of transfer probability measure. This study finds the expected return of foreign stock index in the no arbitrage condition, in addition equal to foreign forward interest rate with the same period , must be add a correction term to reflect the exchange rate risk and the transfer of forward martingale measure. This paper also derives the pricing formula of equity swaptions¡Bcaps¡Bfloors¡Bvariable notional principal and blended equity swap. Finally, we find the volatility of foreign forward interest rate is the most important factor of pricing the swap rate from numerical simulation. And if the correlation of the volatility of exchange rate and foreign stock index¡Bthe correlation of the volatility of exchange rate and foreign forward interest rate are negative, the swap rate will be higher.

無匯率風險之跨通貨股權交換是新型態的衍生性金融商品,投資人可用此從事跨國投資,而不承擔匯率風險.本文立基於Dravid,Richardson and Sun(1993), Amin and Bodurhta(1995), 及Lin(1997), 首次推導間斷時間,可計算之無匯率風險下跨通貨單向及雙向股權交換之評價模型.在現金流量法之下,股價指數及匯率的隨機過程設定為lognormal process,利率則跟隨HJM模型.文中發現影響無匯率風險之跨通貨股權交換價格的主要變數為股價指數的波動度,外國股價指數與匯率間的相關性,以及兩國利率差距,與匯率的波動度無關.最後,以三個例子說明此新型態金融工具之運作情形. 1. Preliminary....................................................................................................................................................................1 1.1 Background...............................................................................................................................................................1 1.2 Brief Literature Review on the Pricing of Equity Swaps...........................................................................................3 1.3 The Aim of This Study.............................................................................................................................................4 1.4 Chapter Outline and Results......................................................................................................................................5 2.Introduction to Equity Swaps..........................................................................................................................................7 2.1 Basic Equity Swaps...................................................................................................................................................7 2.2 Variants of Baisc Equity Swaps...............................................................................................................................11 2.3 International Investment Environments....................................................................................................................12 2.4 Cross-Currency Equity Swaps.................................................................................................................................14 3. Literature Review...........................................................................................................................................................19 3.1 Marshall,Sorensen, and Tucker(1992)......................................................................................................................19 3.2 Rich(1995)................................................................................................................................................................20 3.3 Jarrow and Turnbull(1996).......................................................................................................................................22 3.4 Lin(1997)..................................................................................................................................................................25 3.5 Chance and Rich(1998).............................................................................................................................................27 4. Valuation of Cross-Currency Two-Way Equity Swaps Without Currency Risks Under Constant Interest Rates.........35 5. Valuation of Cross-Currency Two-Way Equity Swaps Without Currency Risks Under Stochastic Interest Rates.......43 6. Valuation of Cross-Currency One-Way Equity Swaps Without Currency Risks..........................................................55 7. Case Study......................................................................................................................................................................61 7.1 Case One...................................................................................................................................................................61 7.2 Case Two..................................................................................................................................................................63 7.3 Case Three.................................................................................................................................................................64 8. Conclusions...................................................................................................................................................................67 Appendixes........................................................................................................................................................................69 References .........................................................................................................................................................................92 / Based on Dravid,Richardson, and Sun(1993), Amin and Bodurtha(1995), and Lin(1997), this thesis first derives the computable discrete-time pricing formulas for the cross-currency one-way and two-way equity swaps without currency risks, which are exotic financial derivatives used for cross-border investments without the exchange rate exposure. Under the cash flow approach, equity indexes and the exchange rate are modeled by the lognormal processes, and the interest rate processes follow the HJM model. The swap price is shown to depend on the volatilities of equity indexes, the interaction between the foreign equity index and the exchange rate, as well as the interest rate differential of two countries. It does ont depend on the volatility of the exchange rate. Finally, three cases illustrate the usage of these two exotic financial instruments.

The eruption of the financial crisis in 2008 caused immense widening of both domestic and cross currency basis spreads. Also, as a majority of all fixed income contracts are now collateralized the funding cost of a financial institution may deviate substantially from the domestic Libor. In this thesis, a framework for pricing of collateralized interest rate derivatives that accounts for the existence of non-negligible basis spreads is implemented. It is found that losses corresponding to several percent of the outstanding notional may arise as a consequence of not adapting to the new market conditions. / I samband med utbrottet av 2008 års finansiella kris vidgades många basisspreadar till ej tidigare skådade nivåer. Därtill krävs i dagsläget att säkerhet finns tillgänglig vid initieringen av en majoritet av alla räntekontrakt, vilket innebär att en banks finansieringskostnad kan avvika substantiellt från den inhemska interbankräntan. I detta examensarbete implementeras ett ramverk för prissättning av räntederivat som beaktar existensen av basisspreadar samt krav på säkerhet. Resultaten visar att förluster motsvarande flera procent av det nominella beloppet kan uppstå som konsekvens av att inte anpassa sig till det nya tillståndet på räntemarknaden.

The global financial crisis of 2007 caused abrupt changes in the financial markets. Interest rates that were known to follow each other diverged. Furthermore, both regulation and an increased awareness of counterparty credit risks have fuelled a growth of collateralised contracts. As a consequence, pre-crisis swap pricing methods are no longer valid. In light of this, the purpose of this thesis is to apply a framework to the Swedish swap market that is able to consistently price interest rate and cross currency swaps in the presence of non-negligible cross currency basis spreads, and to investigate the pricing differences arising from the use and type of collat- eral. Through the implementation of a framework proposed by Fujii, Shimada and Takahashi (2010b), it is shown that the usage of collateral has a noticeable impact on the pricing. Ten year forward starting swaps are found to be priced at lower rates under collateral. Moreover, the results from pricing off-market swaps show that disregarding the impact of collateral would cause one to consistently underestimate the change in value of a contract, whether in or out of the money. The choice of collateral currency is also shown to matter, as pricing under SEK and USD as the collateral currencies yielded different results, in terms of constructed curves as well as in the pricing of spot starting, forward starting and off-market swaps. Based on the results from the pricing of off-market swaps, two scenarios are outlined that exemplify the importance of correct pricing methods when terminating and novating swaps. It is concluded that a market participant who fails to recognise the pricing implications from the usage and type of collateral could incur substantial losses. / Finanskrisens utbrott år 2007 orsakade abrupta förändringar i finansmarknaden. Räntor som tidigare följt varandra divergerade. Vidare gav både reglering av finansmarknaden och en ökad medvetenhet om motparters kreditrisk upphov till en tillväxt av kontrakt med ställda säkerheter. Följaktligen är det inte längre korrekt att prissätta swappar enligt metoder från tiden före finanskrisen. Mot bakgrund av detta är syftet med denna uppsats att applicera ett ramverk på den svenska swapmarknaden som på ett konsekvent sätt kan prissätta ränte- och valutaswappar med icke negligerbara räntespreadar, samt att undersöka prisskillnaderna som uppstår från användandet och typen av ställda säkerheter. Genom implementering av ett ramverk av Fujii, Shimada och Takahashi (2010b) visar denna studie att användandet av ställda säkerheter har en noterbar påverkan på prissättningen. Swappar med tio års löptider och framtida startdatum prissattes lägre när ställda säkerheter inkluderades i prissättningen. Vidare visar resultaten från prissättningen av off-market swappar att genom att bortse från effekten av ställda säkerheter så undervärderas ett kontrakts värdeförändring genomgående, oavsett om kontraktet är in the money eller out of the money. Valet av valuta på de ställda säkerheterna visade sig också spela roll, då prissättningen med SEK och USD som säkerhetsvalutor gav olika resultat i termer av konstruerade kurvor och i prissättning av spot-startande, framtida startande och off-market swappar. Baserat på resultaten ovan genererades två scenarion som påvisade vikten av en korrekt prissättningsmetod vid byte av motpart eller stängning av en swap. Härifrån dras slutsatsen att en marknadsaktör som inte inser vilken påverkan valet av ställda säkerheter har på prissättningen kan drabbas av betydande förluster.

隨著大陸地區的改革開放，在外資不斷湧入，經濟不斷成長的情況下，新金融商品在大陸之發展越來越茁壯；目前，大陸地區的新金融商品之發展，慢慢與國際接軌，朝金融多樣化的目標前進。本文分別列舉一個大陸地區的法人金融產品與個人理財產品為例，進行個案評價與分析。 在法人金融產品方面，本文以中國銀行發行的美元收匯保值方案為例，進行分析。此商品屬於換匯換利的一種，茲命名為區間利差匯率交換合約，並以cLFM為評價模型，配合參數化的校準方法，進行遠期利率的模擬。透過評價結果可知，雖然產品的條款設定較高的交換匯率，對投資人有利；但參考利率之走勢卻不利於投資人；因此，不論是投資人或機構法人購買此類商品時，應深入瞭解產品的條款與其涵義，從財務分析的角度思考購買產品的必要性。 在個人理財產品方面，本文以中國銀行發行的美元日進斗金商品為利，進行分析。本商品屬於組合式外幣存款的一種，以存入固定金額的外幣，做為本金；利息連動的部分，則係與歐元兌美元的每日多區間選擇權進行連動；投資人購買此商品除了可保本，更具有1%的保息效果。透過評價可知，由於條款設定較優，使得發行商的利潤較低，只有1.1996%的收益率，劣於同類型發行於台灣的產品。不過，大陸的地大物博、人口眾多，定期存款也高出台灣許多；故在早期，市場上同類型產品不多的情況下，發行商可靠著薄利多銷的方式，進行組合式外幣存款的銷售，藉由量的效果增加收益來源，並達到改善銀行外幣資產不足的目的。 目前，大陸地區出現結構型商品同質化嚴重的問題；因此，對我國的金融機構而言，若未來有意進軍大陸市場，應藉由我們已累積的金融服務經驗為基礎，在一片紅海市場中，從台灣經驗中建構出的藍海市場，朝亞太金融中心與籌資中心的目標前進。

In this study we analyse relationship between classical approach to valuation of linear interest rate derivatives and post-crisis approach when the valuation better reflects credit and liquidity risk and economic costs of the transaction on top of the risk-free rate. We discuss the method of collateralization to diminish counterparty credit risk, its impact on derivatives pricing, and how overnight indexed swap (OIS) rates became market standard for discounting future derivatives' cash flows. We show that using one yield curve to both estimating the forward rates and discounting the expected future cash flows is no longer possible in arbitrage free market. We review in detail three fundamental interest rate derivatives (interest rate swap, basis swap and cross-currency swap) and we derive discount factors used for calculating the present value of expected future cash flows that are consistent with market quotes. We also investigate drivers behind basis spreads, in particular, credit and liquidity risk, and supply and demand forces, and show how they impact valuation of derivatives. We analyse Czech swap rates and propose an estimation of CZK OIS curve and approximate discount rates in case of cross-currency swaps. Finally, we discuss inflation markets and consistent valuation of inflation swaps.

The world is moving towards real-time – and so are payments. A global transformation of payments is lying ahead, and the future offers instant payments in multiple currencies, around the clock, every day of the year. Introducing a new platform that permits instant payments for cross-currencies will change the traditional business for banks and their corporate customers. Since this payment solution is first of its kind, it will become difficult for banks to predict the future needs of their corporate customers, but they do need to find new ways to create value. Moreover, the rise of a more network-centric way of doing business pressures banks into finding new partnerships and break the traditions of incremental improvements. This study aims to investigate how instant payments for cross-currencies influence the interplay of value creation between banks and their corporate customers. It further aims to understand how the need for co-opetition will affect banks’ value creation towards their corporate customers while maintaining a competitive position in the future of payments. Through an empirical study, survey findings, and a review of existing literature, an exploratory study was performed. The results implied that the amount of value created depends on the company’s size, target market, geographical location, transaction intensity, and degree of international relationships. Furthermore, the value can differ for different units within each company; for instance, closeness to end-consumer. A resistance to changing routines and systems was identified, which must be stabilized before the payment solution can properly be utilized. To grasp the new business opportunities emerging for banks, they must continuously sense the balance between customers’ willingness to pay and new value offerings. Suggestively by embedding it into a familiar presence and/or gradual implementation by providing an opportunity to choose among payment solutions. Besides, the future of payments will increasingly involve attention to the core business, availability, and providing customized support. Also, co-opetition was shown to be a promising strategy in many aspects, since the future of payments will be shared with more actors than ever before. However, common trading zones will arise and blur the national boundaries, which result in that partnerships initially taking the form of collaboration will, over time, progress into a coopetition relationship. On top of that, cross-border issues in terms of cultural mismatches, different traditions, as well as integrating different businesses and operating models, might obstruct the progression. Some products or actors depend on other functionalities to grow, and for instant payments for cross-currencies to reach its full potential, all actors and regulations involved need to be aligned. / Världen går mot realtid - och det gäller även betalningar. En global förändring av betalningar kommer att ske, och framtiden erbjuder realtidsbetalningar i flera valutor dygnet runt, året om. Att introducera en ny plattform som tillåter omedelbara betalningar i flera valutakurser kommer att förändra den traditionella verksamheten för både banker och deras företagskunder. Eftersom denna betalningslösning är den första i sitt slag kommer det att bli svårt för bankerna att förutsäga deras kunders framtida behov och de måste hitta nya sätt att skapa värde på. Dessutom bidrar ökningen av ett mer nätverkscentrerat sätt att göra affärer att bankerna är mer pressade till att hitta nya partnerskap och bryta gamla traditioner av inkrementella förbättringar. Denna studie syftar till att undersöka hur omedelbara betalningar inom flera valutor påverkar samspelet i värdeskapandet mellan banker och deras företagskunder. Vidare avser den förstå hur behovet av co-opetition kommer att påverka bankers värdeskapande gentemot sina företagskunder samtidigt som man behåller en konkurrensposition i framtidens betalningar. Denna studie utfördes som en empirisk studie genom intervjuer, enkätsvar och granskning av befintlig litteratur. Resultaten antydde att värdet som skapas beror på företagets storlek, marknad, geografiska läge, transaktionsintensitet och graden av internationella relationer. Dessutom kan värdet variera för olika enheter inom ett och samma företag; till exempel närheten till slutkonsument. Ett motstånd till att förändra rutiner och system identifierades, vilket måste stabiliseras innan betallösningen kan nå sin fulla potential. För att ta sig an de nya affärsmöjligheter som uppstår för bankerna måste de kontinuerligt urskilja balansen mellan kundernas betalningsvillighet och nya värdeerbjudanden. Detta kan förslagsvis göras genom att bädda in en ny lösning i en mer välbekant skepnad och/eller gradvis implementera innovationen genom att erbjuda en möjlighet att välja mellan betalningslösningar. Därtill kommer betalningarnas framtid i allt högre grad att innebära större satsningar på att arbeta med kärnverksamhet, tillgänglighet och att tillhandahålla personifierad support. Dessutom visade sig co-opetition vara en lovande strategi i flera aspekter, eftersom betalningens framtid kommer att delas med fler aktörer än någonsin. Gemensamma handelszoner kommer emellertid att uppstå och sudda ut de nationella gränserna, vilket resulterar i att partnerskap som ursprungligen tar formen av samarbete kommer med tiden att utvecklas till co-opetition. Dessutom kan samarbete över landgränser utmanas av kulturella missförhållanden, olika traditioner samt integrering av olika företag och operativa modeller vilket kan hindra utvecklingen. Då vissa produkter eller aktörer är beroende av andra funktionaliteter för att växa, och för att realtidsbetalningar i flera valutor ska nå sin fulla potential, måste alla aktörer och förordningar vara i linje.

雖然跨通貨股酬交換在國際投資市場扮演著重要的角色，但文獻上關於股酬交換評價模式的相關探討並不多，且多集中於國內市場或以本國貨幣做為支付幣別的股酬交換。對於跨通貨股酬交換而言，其評價模式較國內股酬交換之評價模式複雜許多，如何將影響其價值之股價指數、匯率與利率此三個主要因子間的交互相關性同時加入考量，即是此產品之評價過程的重點。 本文在完全市場的假設下，同時放寬傳統評價方法之各變數之相關係數為固定值的假設，提出一新的股酬交換評價方法，即以『兩階段兩步驟』之較具經濟含意的複製方式，推導出股酬交換的一般化評價公式。透過此複製方法，可更清楚得知股酬交換於存續期間的價值變動，更可進一步求得其避險方式，以提供股酬交換交易商在面臨不對稱風險(mismatch risk)時的避險方法。而本文的第二個貢獻在於，將本文所提出之『兩階段兩步驟』的複製方法應用於利率交換的評價上，推導出跨通貨利率交換的一般化評價模式，以進一步比較股酬交換與利率交換此兩種商品的差異性，並試圖釐清市場上對於跨通貨股酬交換評價上的誤解。 與傳統評價公式最大的差異在於：本文評價公式額外考慮了一修正項，複製投資組合可藉由此修正項，對未來各參數間的變動隨時做出調整，以使投資組合能完全複製跨通貨股酬交換的價值。 本文發現，對於國內投資人支付固定利率，以交換B市場的股價指數報酬，且以C國的貨幣做為支付幣別的跨通貨股酬交換而言，其價值除了受到當期利率期間結構的影響外，在期初或每期交換後，其價值與股價指數無直接關聯，但在兩支付間，其價值則會受到當時股價指數與前期股價指數之相對比例的影響。同時，C國對本國的未來匯率並未直接影響跨通貨股酬交換的價值。且若假設各國遠期利率的波動度為零下，則當B國股價指數與C國對本國的匯率呈現正關係或當B國股價指數與B國對本國的匯率呈現負關係時，跨通貨股酬交換的價值愈大。另外，市場上投資人通常誤認股酬交換的價值等於利率交換價值，對於股酬交換與利率交換的比較，本文發現在大多數的情況下，股酬交換的價值與利率交換的價值並不相等。

在WTO成立，各國國際化程度日益提高的同時，企業與個人進行跨國投資的情形也愈來愈普遍，跨國投資除了要考慮標的資產之報酬與波動性之外，尚須考量匯率變動所產生之風險與不確定性。當某一國外資產具有正向預期報酬率的同時，實現後的報酬率卻又不一定為正，正是因為匯率波動所產生的影響。又，傳統財務理論告訴我們，藉由增加投資組合中所有非完全正相關的資產個數可以有效的降低投資組合的非系統風險，因此投資人在進行投資時往往採用建構投資組合的方式取代持有少數資產的型態。然而，在建構跨通貨避險投資組合時，若是對於投資組合中的各項資產與外幣分別進行避險（分別利用衍生性商品避險），往往是費時、費力又不具有效率。因此，對於整個投資組合進行避險反而是一個比較好的方法，當投資組合價值發生變動時，可以即時對於各項資產部位與外幣分別做調整，遠較於對個別資產進行避險來的方便、快速且有效。 / In most cases, investment is made of building a portfolio rather than single asset. Therefore, it is necessary to develop techniques of valuing portfolio derivatives. Moreover, we consider a cross-currency portfolio that account for currency and interest rate risk. As interest rate is stochastic, we use Heath-Jarrow Morton (HJM) Approach to describe its dynamics. Applying Vorst (1992); Geman, Karoui and Rochet(1995), we derive the approximated close-form of the cross-currency portfolio option. In HJM Approach, it is difficult to acquire hedge ratios of options. We apply another method to build a hedging portfolio. Then, we perform numerical simulations to test its hedging efficiency and sensitivity with respect to different variables.